Development and Evaluation of 2D and 3D Image Quality Metrics. Simon Nicholas Murphy. Graduate Program in Medical Physics Duke University

Transcription

1 Development and Evaluation of 2D and 3D Image Quality Metrics by Simon Nicholas Murphy Graduate Program in Medical Physics Duke University Date: Approved: Ehsan Samei, Supervisor James T. Dobbins, III Jennifer C. O'Daniel Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Graduate Program in Medical Physics in the Graduate School of Duke University 2011

2 ABSTRACT Development and Evaluation of 2D and 3D Image Quality Metrics by Simon Nicholas Murphy Graduate Program in Medical Physics Duke University Date: Approved: Ehsan Samei, Supervisor James T. Dobbins, III Jennifer C. O'Daniel An abstract of a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Graduate Program in Medical Physics in the Graduate School of Duke University 2011

3 Copyright by Simon Nicholas Murphy 2011

4 Abstract With continuing advances in medical imaging technologies, there is an increased demand to extract quantitative information from images. This has been particularly vital in the effort to increase the efficacy and accuracy of diagnoses. Quantitative information is readily available in images because the acquisition techniques intrinsically involve physical processes. Quantitative image quality metrics are critical in the evaluation of medical images for diagnostic merit, particularly when used for the characterization and comparison of different systems. When such metrics are based on measurable physical parameters, they can provide valuable information for system optimization. Image quality describes the goodness of an image in displaying information for a task. This thesis explored methods of measuring image quality for two scenarios: (1) to characterize 2D flat-panel detector performance and (2) to measure directional spatial resolution for 3D images from breast tomosynthesis. In the first chapter, two new wireless digital receptors (DRX-1C and DRX-1, Carestream Health, Inc., Rochester, NY) were evaluated and compared to a conventional flat-panel detector (Pixium 4600, Trixell, Moirans, France) on the basis of detective quantum efficiency (DQE). A secondary goal was also to evaluate the filtration to achieve specified beam qualities for the DQE measurements, closely following the methodology of the International Electrotechnical Commission (IEC) for radiation iv

5 qualities RQA5 and RQA9. All three DR systems demonstrated similar modulation transfer functions (MTFs) at most frequency ranges, while the DRX-1 showed lower values near the cutoff of approximately 3.5 cycles/mm. At each exposure, the Pixium 4600 and DRX-1C demonstrated similar noise power spectrum (NPS) curves that indicated better noise performance than the DRX-1. Zero-frequency DQEs for Pixium 4600, DRX-1C, and DRX-1 were approximately 63%, 74%, and 38% for RQA5 and 42%, 50%, and 28% for RQA9, respectively. In terms of DQE performance, the DRX-1C image receptor was found to be superior to the Pixium 4600 and DRX-1. In the second chapter, the directional spatial resolution of simulated breast tomosynthesis images was determined using a cone-based technique and a sphere phantom. Projections were simulated for a voxelized breast phantom with 12 mm diameter sphere inserts using a fluence modeled from a 28 kvp beam incident upon an indirect flat-panel detector with 200 µ m pixel size. Characteristic noise and blurring for each projection were added using cascaded systems analysis. The projections were reconstructed using a standard filtered backprojection technique, producing a 3D volume with an isotropic voxel size of 200 µ m. Regions of interest (ROIs) that completely encompassed single spheres were extracted, and conical regions were prescribed along the three axes extending from the centroid. Voxels within a cone were used to form an edge spread function (ESF), from which the directional MTF was calculated. A bin size of 0.02 mm and a conical range of 30 degrees were found optimal v

6 for maximizing accuracy and minimizing noise of the MTF. A method for removing outof-plane artifacts of the ESFs along in-plane axes was investigated and yielded a modified MTF. The idea of separating the effective resolution and artifacts from the measured ESF are expected to facilitate the interpretation of MTF measurements in breast tomosynthesis. Similar methods may be applied to characterize the spatial resolution of other 3D imaging modalities. vi

7 Contents Abstract... iv List of Tables... x List of Figures... xi Acknowledgements... xiii I. Evaluation of 2D Digital Image Receptors... 1 I.1 Introduction... 1 I.2 Materials and Methods... 3 I.2.i. Detectors... 3 I.2.ii. Beam Characterization... 3 I.2.ii.a. X-ray Techniques... 3 I.2.ii.b. Data Linearization... 4 I.2.ii.c. Spectral Simulation... 5 I.2.iii. DQE Measurements... 6 I.2.iii.a. Modulation Transfer Function... 6 I.2.iii.b. Noise Power Spectrum... 7 I.2.iii.c. DQE Calculation... 8 I.3 Results... 9 I.3.i. Data Linearization... 9 I.3.ii. Spectral Simulation... 9 I.3.iii. Modulation Transfer Function vii

8 I.3.iv. Noise Power Spectrum I.3.v. Detective Quantum Efficiency I.4 Discussion I.4.i. Comparisons of Detectors I.4.ii. Comparisons of Filtrations I.4.iii. Implications of Wireless DR I.5 Conclusions II. Directional MTF for Breast Tomosynthesis II.1 Introduction II.2 Materials and Methods II.2.i. Image Simulation II.2.ii. Uncorrected MTF II.2.iii. Theoretical Directional MTF II.2.iv. Modified MTF II.2.v. Preliminary Experimental Validation II.3 Results II.3.i. Reconstruction II.3.ii. Theoretical MTF II.3.iii. Uncorrected MTF II.3.iv. Comparison of Theoretical and Simulated MTFs II.3.v. Modified MTF for x and y II.3.v. Preliminary Experimental Validation viii

9 II.4 Discussion II.4.i. Evaluation of Cone-based Method II.4.ii. Separation of Artifact and Resolution Information II.5 Conclusions References ix

10 List of Tables Table 1: Physical Characteristics of Digital Image Receptors... 4 Table 2: Beam Qualities and Required Filtrations... 5 Table 3: Spectral Simulation Results Table 4: Experimental MTF frequency locations for 1 mr exposure Table 5: Estimated DQE values for 1 mr exposure by frequency bins x

11 List of Figures Figure 1: MTF images for DRX-1C detector with radio-opaque edge test device with arrows indicating the horizontal (left) and vertical (right) directions Figure 2: NNPS image for DRX-1C detector indicating the top left ROI that served as the reference for normalizing other ROIs in the image. The ROI array was formed along the directions indicated by the arrows. The heel effect visible along the vertical axis of the detector is an example of small variation in signal across the image Figure 3: Original (left) and linearized (right) system responses for Pixium The linearized system responses were measured from actual images. The offsets are small with respect to the slope, sufficient enough for zero-offset conditions Figure 4: Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions. Note the similarities of spectral shapes of the normalized spectra (right). Also note the significant differences in fluence between filtrations in the simulated spectra (left) Figure 5: MTF results by detector (columns) and beam quality (rows) Figure 6: Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships between detectors (blue, red, and green) and by filtration (solid and dashed) Figure 7: NNPS results by detector (columns) and beam quality (rows) Figure 8: Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mr exposure showing the relationships between detectors (blue, red, and green) and by filtration (solid and dashed) Figure 9: DQE results by detector (columns) and beam quality (rows) Figure 10: Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mr exposure showing the relationships between detectors (blue, red, and green) and by filtration (solid and dashed) Figure 11: DRX1-C NNPS images at 1 mr for RQA5 with IEC filtration (left) and alternative filtration (right). Images are equally windowed at 45 and leveled at Figure 12: Depiction of the virtual image system xi

12 Figure 13: Example of 30-degree cone prescribed along z axis of the sphere Figure 14: Photograph of the imaging system with the acrylic sphere phantom embedded in oil Figure 15: View of the central slice of the breast phantom reconstruction before (top) and after (bottom) background subtraction. The z axis is through the page Figure 16: 3D rendering of the ROI volume (left) and cross-sectional views of the most centrally located sphere with centroid indicated with red circle (right) Figure 17: Theoretical 3D MTF results along the three major planes (top) and along x, y, and z directions (bottom). Also note that the angular spread seen in the fx-fz plane is equal to the angular range of 44 for the acquisition Figure 18: Uncorrected ESF (top), LSF (middle), and MTF (bottom) for x, y, and z directions Figure 19: Comparisons of the directional MTFs as calculated by the sphere method (dashed line), by theoretical line profiles (light-weight line), by theoretical cone regions (heavy-weight line) Figure 20: Modified ESF (top), LSF (middle), and MTF (bottom) for x and y directions. 43 Figure 21: Cross sectional views of the experimental sphere image with centroid indicated with red circle Figure 22: ESF (top), LSF (middle), and MTF (bottom) of real image for x, y, and z directions xii

13 Acknowledgements I would like to thank Ian Yorkston, Mark Purdum, and Van Huston of Carestream Health, Inc., (Rochester, NY) for their help with digital detector measurements. I would also like to thank Olav Christianson, Samuel Richard, Brian Harrawood, and Max Amurao for their assistance with collecting data and analyzing results. Special thanks go to my committee members for their helpful insights and suggestions for this thesis. Last but not least, I want to express deep appreciation for the support and mentorship provided by my advisor, Dr. Ehsan Samei. xiii

14 I. Evaluation of 2D Digital Image Receptors I.1 Introduction In the past decade, many areas of radiological practice have seen a conversion from screen films to the storage phosphor cassettes of computed radiography (CR) to the active-matrix flat-panel detectors of digital radiography (DR). Both CR and DR are digital systems that offer many potential benefits including, but not limited to, better image quality, wider dynamic range, quicker readout, lower radiation dose, and higher throughput [1-3]. Even with advances in DR technologies such as improved detective quantum efficiency (DQE), the primary radiographic system of today continues to be CR. A major obstacle to completely accepting DR is the high capital cost of acquiring an entire system per examination room while also providing capability for portable applications. Recently, manufacturers like Carestream Health, Fuji, and Toshiba have introduced wireless digital image receptors that can serve as replacements for CR cassettes. As these are new technologies, a further investigation to characterize these detectors is warranted. In the case of radiographic receptors, DQE has historically been the metric of choice [4] because it indicates the ability of the image receptor to convert incident x-ray photons into useable signal essentially a measure of signal-to-noise ratio (SNR) efficiency and overall system performance [2,3]. DQE is observed across a range of spatial frequencies for evaluating how the detector depicts small and large objects [3]. 1

15 DQE metrics have been used in numerous studies to characterize CR phosphor-screens as well as indirect and direct digital detectors [4-11]. The importance of this highly quantitative metric may be implied by the introduction of a DQE measurement standard by the International Electrotechnical Commission (IEC) [12]. The standard measurement methodology of the International Electrotechnical Commission (IEC) pertains to the image quality of 2D digital radiographic detectors. While the IEC formalism is well-developed, some of the components that it requires are not necessarily the most optimal for characterizing DQE. This has been explored in previous studies in terms of filtration material purity, beam limitations, and region of interest (ROI) configuration [13,14]. To reduce the variability in the radiographic output across various x-ray tubes due to inherent filtration differences, the IEC formalism prescribes specific additional aluminum filtration to attain radiation beam qualities based on target half value layers (HVL). Achieving and verifying the desired HVL, however, requires applying a substantial amount of aluminum at the exit window of the x-ray tube, which is often directed toward the ground. This can be a logistical inconvenience and can increase the risk of damage to the image receptor and measurement equipment. Similar beam qualities, on the other hand, may be attained more conveniently using a thinner, lighter filtration combination utilizing a higher Z number material. Care is warranted, however, as a previous study [6] had indicated that the choice of filtration material could impact the DQE. 2

16 The purpose of this study was two-fold. First, we aimed to evaluate and compare two wireless image receptors with a conventional flat-panel detector on the basis of DQE performance. Second, we compared DQE results using the IEC-prescribed filtration with an alternative filtration. For the latter, an optimum filtration composition was determined and compared with the IEC filtration on the basis of DQE. I.2 Materials and Methods I.2.i. Detectors The physical characteristics of the three digital image receptors evaluated in this study are listed in Table 1. The Pixium 4600 was a conventional digital flat-panel. The DRX-1C and DRX-1 were both wireless digital cassettes that were tethered for the purposes of this study. All detectors were FDA approved and available commercially. Each detector was calibrated according to its manufacturer specifications to correct for gain, offset, and bad pixels. They were all dedicated for non-clinical laboratory research purposes and hence could be operated under service settings that permitted acquisition of raw (i.e. for processing) images. I.2.ii. Beam Characterization I.2.ii.a. X-ray Techniques All measurements for this study were taken with a well-characterized standard radiographic system (Super80CP, Philips Healthcare, Andover, MA). The x-ray tube had an inherent filtration of 2.7 mm Al. Free in-air exposures were measured using 3

17 Table 1: Physical Characteristics of Digital Image Receptors Manufacturer Trixell (Moirans, France) Carestream Health, Inc. (Rochester, NY) Carestream Health, Inc. (Rochester, NY) Detector Pixium 4600 DRX-1C (wireless) DRX-1 (wireless) Detector type Indirect Indirect Indirect Detector material CsI:Tl (CsI) CsI:Tl (CsI) G2O2S:Tb (GOS) Pixel pitch (size) mm mm mm Array size subpanels single panel single panel Imaging area cm cm cm 2 calibrated radiation meters (Mult-O-Meter Type 407, Unfors Instruments AB, Billdal, Sweden) at 183 cm source-to-chamber-distance (SCD). The SCD also corresponded to same plane as the image receptor surface. The x-ray output was made to conform to IEC beam quality definitions [12,15] on the basis of half value layer (HVL) and peak kilovoltage setting using an aluminum filtration (type-1100, 99% purity) and an alternative filtration consisting of copper (UNS C11000, 99.9% purity) and aluminum (type-1100, 99% purity). The IEC radiation quality numbers (RQA) used in this study are summarized in Table 2. HVLs were determined by iteratively adding successive thicknesses of aluminum until reaching reduced exposure levels within a tolerance of [12]. As for the alternative filtration, the aluminum was placed downstream of the copper filter to attenuate characteristic radiation peaks from copper at approximately 9 kev. I.2.ii.b. Data Linearization The system response function was determined for each detector and filtration combination by acquiring flat-field images at increasing photon fluence until just before 4

18 Table 2: Beam Qualities and Required Filtrations IEC Radiation Quality Number Peak kilovoltage Required HVL Required IEC Filtration Actual IEC Filtration Alternative Filtration RQA5 70 kvp 7.1 mm Al 21 mm Al 21 mm Al* RQA9 120 kvp 11.5 mm Al 42 mm Al 40 mm Al* 0.5 mm Cu mm Al* 1.04 mm Cu mm Al* * For reasons of convenience, these will be referred to as RQA5A, RQA5C, RQA9A, and RQA9C. saturation levels. To avoid the influence of detector backscatter on exposure measurements, a relationship for each filtration was first determined for two radiation meters. A target meter was placed at the central axis and a reference meter was placed at the edge of the light field (large enough to cover the detectors). The reference meter served as a surrogate for the target meter to avoid direct exposure measurements in the plane of the image receptor. Exposure relationships were determined before each measurement set (i.e., detector and filtration combination) to account for changes in temperature, pressure, and humidity. The system response function was calculated by using a regression of ADU (pixel value) versus exposure. Images acquired for each series were then converted to achieve a linear response with zero offset and scaled to achieve high quantization (adequate dynamic range). Linearization of the detector responses ensured that zero exposure corresponded to zero pixel value. I.2.ii.c. Spectral Simulation The effects of additional filtration on x-ray output spectra were observed with spectral simulation software (XSPECT V4.0, Henry Ford Hospital, Detroit, MI). To more 5

19 adequately describe the performance of a typical X-ray generator, inherent filtration of 3 mm oil, 1.48 mm Pyrex glass, and 2 mm aluminum was input into the simulation in addition to the filters of interest. The ideal signal to noise ratio squared, or incident photon fluence per exposure (q), was estimated for each filtration by integrating the energy-dependent photon counts per unit exposure over all energy bins. I.2.iii. DQE Measurements The assessment of the linearized images followed the formalism described by IEC for measuring the DQE [12]. For this study, the normal exposure level XN was set at 1 mr to the detector surface, as measured at the central axis perpendicular to the anode-cathode axis. I.2.iii.a. Modulation Transfer Function Spatial resolution was characterized by evaluating the presampled modulation transfer function (MTF) along directions parallel (vertical) and perpendicular (horizontal) to the anode-cathode axis using the angled-edge method [6-10,13]. A radioopaque edge test device [7] was placed in the center of the field at a pitch of approximately 30:1 (about 2 ) to the axis perpendicular to that being measured, as shown in Figure 1. External lead apertures were not used [6]; instead, the internal collimation from the radiographic unit was used to collimate the beam to the detector area. Raw images were acquired of the edge with the normal exposure level XN of 1 mr at the detector face. The procedure of calculating the MTF followed previously described 6

20 methods [6-10,13]. The edge spread function (ESF) was determined along lines crossing the edge of the angled test device. The derivative of the ESF was calculated to form the line spread function (LSF), to which a Hanning filter was applied. The MTF was then calculated as the fast Fourier transform (FFT) of the LSF and normalized at the zerofrequency axis. To conform to IEC guidelines, the MTF was resampled into frequency steps of 0.05 cycles/mm [12]. Figure 1: MTF images for DRX-1C detector with radio-opaque edge test device with arrows indicating the horizontal (left) and vertical (right) directions. I.2.iii.b. Noise Power Spectrum Noise amplitude and texture were characterized by determining the normalized noise power spectrum (NNPS), which was evaluated with flat field exposures at approximate exposure levels of XN/2, XN, and 2XN (0.5, 1.0, and 2.0 mr) to the image receptor surface. Analysis of the flat-field images followed previously defined methods [4,14,15] using over 4 million independent pixels with regions of interest (ROIs) of size 7

21 128x128. The NNPS images were detrended using a quadratic (second order) background subtraction. Small variations in exposure across ROIs were corrected by normalizing pixel values of each ROI to the mean value in the top left ROI, as shown in Figure 2. The NNPS was then calculated with the 2D FFT including the zero-frequency axes corresponding to the horizontal and vertical directions. The results were then resampled using 0.05 frequency bins according to IEC guidelines [12]. Figure 2: NNPS image for DRX-1C detector indicating the top left ROI that served as the reference for normalizing other ROIs in the image. The ROI array was formed along the directions indicated by the arrows. The heel effect visible along the vertical axis of the detector is an example of small variation in signal across the image. I.2.iii.c. DQE Calculation The DQE was calculated using the following relationship [6,15]: 8

22 where the frequency-dependent MTF and NNPS were determined as described in previous sections, X was the exposure value in mr corresponding to the NNPS image, and q was the ideal signal to noise ratio squared in units of photons mm -2 mr-1 as estimated from the spectral simulations. I.3 Results I.3.i. Data Linearization The detectors in this study provided raw ADU (or pixel) values in a linear scale. The data were converted using the following system conversion function: where Q(i,j) is the raw image data, m and b are slope and intercept parameters obtained from linear regression of the system response function, and I(i,j) is the linearized scaled data. The factor of 1000 was found to scale I(i,j) such that the maximum value was a large 16-bit number. Figure 3 shows the original and linearized system responses for the Pixium Note that the y-intercepts of the regressions for the linearized responses are negligible (< 0.1%) with respect to the slopes, a sufficient condition for zero offset considerations. I.3.ii. Spectral Simulation The spectral simulations of the IEC filtrations and alternative filtrations indicate many similarities in their effective energies, HVLs, and overall shapes of normalized spectra. Results are summarized in Table 3. 9

23 RQA9C ADU ADU RQA9A ADU ADU RQA5C ADU ADU RQA5A ADU ADU Pixium 4600 Original System Response Pixium 4600 Linearized System Response y = x R² = Exposure (mr) y = x R² = Exposure (mr) y = x R² = Exposure (mr) y = x R² = Exposure (mr) Figure 3: Original (left) and linearized (right) system responses for Pixium The linearized system responses were measured from actual images. The offsets are small with respect to the slope, sufficient enough for zero-offset conditions y = 1000x R² = Exposure (mr) y = x R² = Exposure (mr) y = 1000x R² = Exposure (mr) y = 1000x R²= Exposure (mr)

24 Beam Quality Table 3: Spectral Simulation Results Filtration Mean Energy (kv) Photon Fluence (#/mr/mm 2 ) RQA5A 21 mm Al RQA5C 0.5 mm Cu mm Al % diff 0.55% 0.004% RQA9A 40 mm Al RQA9C 1.04 mm Cu mm Al % diff 0.52% 0.25% photons mas -1 cm E E E E E E E E E+04 RQA5 Spectra Comparison 0.5 mm Cu mm Al 21 mm Al 0.0E kev RQA9 Spectra Comparison RQA5 Normalized Spectra Comparison 0.5 mm Cu mm Al 21 mm Al kev RQA9 Normalized Spectra Comparison photons mas -1 cm E E E E E E E E E E mm Cu mm Al 40 mm Al 0.0E kev Figure 4: Spectral simulations for RQA5 (top) and RQA9 (bottom) conditions. Note the similarities of spectral shapes of the normalized spectra (right). Also note the significant differences in fluence between filtrations in the simulated spectra (left) mm Cu mm Al 40 mm Al kev 11

25 I.3.iii. Modulation Transfer Function The limiting spatial resolutions of the systems were indicated by the cutoff frequencies, which were approximately 3.5 cycles/mm for all three detectors. The spatial resolutions also demonstrated a good degree of isotropy, as confirmed by the close alignment of MTF curves between vertical and horizontal directions, differentiated in Figure 5 by dashed and solid lines, respectively. The MTF curves for the Pixium 4600 and DRX-1C were nearly equal to each other, whereas the DRX-1 MTF curve showed a more rapid decrease at high frequencies as shown in Figure 6. This difference may be due to the differences in the inherent optical properties of the scintillating materials, where finer image details are provided by structured CsI more than by granulated GOS. There were no significant differences in MTF curves across beam qualities and filtrations, as shown by the curve comparisons in Figure 6, although the alternative filtration produced slightly higher MTF curves as seen in Figure 4. Table 4 lists the experimental specific spatial frequencies for varying levels of MTF. I.3.iv. Noise Power Spectrum The noise characteristics are indicated by the NNPS curves shown in Figure 7. The noise was similar for both horizontal and vertical directions. As exposure increased, the NNPS decreased, consistent with the characteristics of Poisson noise describing the relationship between signal and noise in the presence of increased photon fluence. At 12

26 RQA9C RQA9A RQA5C RQA5A MTF Pixium 4600 DRX-1C DRX MTF 0.5 MTF MTF 0.5 MTF 0.5 MTF MTF 0.5 MTF 0.5 MTF MTF 0.5 MTF 0.5 MTF horizontal vertical Figure 5: MTF results by detector (columns) and beam quality (rows). 13

27 1.0 MTF MTF Spatial Freq (mm -1 ) RQA5A-Pixium RQA5C-Pixium RQA5A-DRX-1C RQA5C-DRX-1C RQA5A-DRX-1 RQA5C-DRX-1 MTF Spatial Freq (mm -1 ) RQA9A-Pixium RQA9C-Pixium RQA9A-DRX-1C RQA9C-DRX-1C RQA9A-DRX-1 RQA9C-DRX-1 Figure 6: Plots of MTF for RQA5 (top) and RQA9 (bottom) showing the relationships between detectors (blue, red, and green) and by filtration (solid and dashed). 14

28 RQA9C RQA9A RQA5C RQA5A 1E-4 Pixium 4600 DRX-1C DRX-1 1.E-4 1.E-4 1E-5 1.E-5 1.E-5 NNPS NNPS NNPS 1E-6 1.E-6 1.E-6 1E-7 1.E-7 1.E-7 1.E-4 1.E-4 1.E-4 1.E-5 1.E-5 1.E-5 NNPS NNPS NNPS 1.E-6 1.E-6 1.E-6 1.E-7 1.E-7 1.E-7 1.E-4 1.E-4 1.E-4 1.E-5 1.E-5 1.E-5 NNPS NNPS NNPS 1.E-6 1.E-6 1.E-6 1.E-7 1.E-7 1.E-7 1.E-4 1.E-4 1.E-4 1.E-5 1.E-5 1.E-5 NNPS NNPS NNPS 1.E-6 1.E-6 1.E-6 1.E-7 1.E-7 1.E mr - horizontal 0.5 mr - vertical 1.0 mr - horizontal 1.0 mr - vertical 2.0 mr - horizontal 2.0 mr - vertical Figure 7: NNPS results by detector (columns) and beam quality (rows). 15

29 1.E-4 NNPS (1 mr) NNPS 1.E-5 1.E-6 RQA5A-Pixium RQA5C-Pixium RQA5A-DRX-1C RQA5C-DRX-1C RQA5A-DRX-1 RQA5C-DRX-1 1.E-7 Spatial Freq (mm -1 ) 1.E-4 NNPS 1.E-5 1.E-6 RQA9A-Pixium RQA9C-Pixium RQA9A-DRX-1C RQA9C-DRX-1C RQA9A-DRX-1 RQA9C-DRX-1 1.E-7 Spatial Freq (mm -1 ) Figure 8: Plots of NNPS for RQA5 (top) and RQA9 (bottom) at 1 mr exposure showing the relationships between detectors (blue, red, and green) and by filtration (solid and dashed). 16

30 RQA9C RQA9A RQA5C RQA5A 0.8 Pixium 4600 DRX-1C DRX DQE 0.4 DQE 0.4 DQE DQE 0.4 DQE 0.4 DQE DQE 0.4 DQE 0.4 DQE DQE 0.4 DQE 0.4 DQE mr - horizontal 0.5 mr - vertical 1.0 mr - horizontal 1.0 mr - vertical 2.0 mr - horizontal 2.0 mr - vertical Figure 9: DQE results by detector (columns) and beam quality (rows). 17

31 0.8 DQE (1 mr) DQE Spatial Freq (mm -1 ) RQA5A-Pixium RQA5C-Pixium RQA5A-DRX-1C RQA5C-DRX-1C RQA5A-DRX-1 RQA5C-DRX-1 DQE Spatial Freq (mm -1 ) RQA9A-Pixium RQA9C-Pixium RQA9A-DRX-1C RQA9C-DRX-1C RQA9A-DRX-1 RQA9C-DRX-1 Figure 10: Plots of DQE for RQA5 (top) and RQA9 (bottom) at 1 mr exposure showing the relationships between detectors (blue, red, and green) and by filtration (solid and dashed). 18

32 higher frequencies, the NNPS curves of the Pixium 4600 and DRX-1 diverge slightly for the different directions, illustrating increased noise in the readout direction (vertical). Differences in the noise characteristics were more apparent among detectors, as shown for 1 mr in Figure 8. The NNPS curve for the DRX-1 was higher in magnitude across the entire frequency range than either the Pixium 4600 or DRX-1C, which both seemed to demonstrate reasonably similar NNPS curves. The higher magnitude noise of the DRX-1 indicates higher relative noise content overall. Closer inspection of the NNPS curves of the Pixium 4600 and DRX-1C detectors in Figure 7 revealed differences in the spacing between the three exposure levels. The gaps between the Pixium 4600 NNPS curves do not correspond to the factor of two differences between each exposure level especially at low- to mid- spatial frequencies, suggesting a higher level of fixed pattern noise additional noise with increasing exposure levels due to ineffective gain map corrections. Between filtration schemes, the differences in NNPS curves for a given beam quality were not substantial, as shown in Figure 7. I.3.v. Detective Quantum Efficiency The DQE results are shown in Figure 9. DQE curves across exposure levels were almost collinear, except for Pixium 4600, and in general could be inferred from the NNPS results. Additionally, the DQE curves demonstrated a relatively linear response with spatial frequencies, as expected for flat-panel detectors [9]. Differences in DQE among detectors were consistent, for the most part, with the type of scintillating material. 19

33 As depicted for 1 mr exposure in Figure 10, differences between Pixium 4600 and DRX- 1C DQE curves correspond to the differences in their NNPS curves. DRX-1 DQE curves were consistently lower than either the Pixium 4600 or DRX-1C curves. The DQE curves for the alternative filtration were consistently higher than those for the IEC filtration, and the most noticeable differences were near the zero-frequency axis. These effects can be both attributed to ineffective gain map correction. DQE values for 1 mr exposure are listed in Table 5. I.4 Discussion I.4.i. Comparisons of Detectors The limiting spatial resolutions of all three detectors were almost exactly the same, considering that their pixel areas were similar in size. The decrease in highfrequency MTF of the DRX-1 compared to the other detectors is probably a result of increased optical blurring due to the differences in the powdered structure of GOS versus the needle-like structure of CsI [2]. The fact that the DRX-1C and Pixium 4600 have comparable MTFs suggests similar scintillator thicknesses, assuming that the materials were processed alike. The noise of the three detectors demonstrated similar trends with each other. The higher NNPS curves of the DRX-1 detector are probably due also to the scintillating material and its operation in converting photons into signal. The conversion process is less efficient because of the less favorable stopping power of the GOS compared to CsI, 20

34 especially with higher energy beams. The noise of the Pixium 4600 and DRX-1C were similar except for the spacing between exposures. The DRX-1C NNPS curve spacing is consistent with a factor of two difference in exposure levels, but the Pixium 4600 has a smaller spacing. The 0.5 mr NNPS curve of the Pixium 4600 is closer to that of the 0.5 mr NNPS curve of the DRX-1C. This demonstrates that at higher exposures, the Pixium 4600 produces a larger amount of additional noise beyond that explained by simple stochastic effects. It suggests bad performance in the gain map corrections. The DQE results indicate SNR properties of each detector. The Pixium 4600 and DRX-1C are comparable for the most part, with the DRX-1C performing slightly better. The DRX-1, as predicted from MTF and NNPS results, has a DQE much lower than either of the previous two. This is a reflection of the detection properties as provided by its scintillator material. The DQE of the DRX-1, however, is comparable to CR image receptors [2]. The mid-frequency dips in the DQE for Pixium 4600 may be due to the optical properties of the CsI phosphor layer, which can affect the MTF in this manner. Because the DQE is calculated by squaring the MTF, this effect at the mid-range frequencies becomes more apparent. The dips may also be further evidence of bad gain map corrections. I.4.ii. Comparisons of Filtrations The alternative filtration closely matches, for the most part, the IEC-based filtration for MTF, NNPS, and DQEs at RQA5 but not at RQA9. The filters do not have 21

35 Table 4: Experimental MTF frequency locations for 1 mr exposure. Detector Pixium 4600 Filtration 50% MTF (mm -1 ) 40% MTF (mm -1 ) 30% MTF (mm -1 ) 20% MTF (mm -1 ) 10% MTF (mm -1 ) RQA5A RQA5C RQA9A RQA9C DRX-1C RQA5A RQA5C RQA9A RQA9C DRX-1 RQA5A RQA5C RQA9A RQA9C Table 5: Estimated DQE values for 1 mr exposure by frequency bins. Detector Filtration DQE(0.0 mm -1 )* DQE(1.0 mm -1 ) DQE(2.0 mm -1 ) DQE(3.0 mm -1 ) Pixium 4600 RQA5A 62% 42% 32% 21% RQA5C 63% 45% 36% 25% RQA9A 41% 27% 30% 13% RQA9C 43% 33% 27% 19% DRX-1C RQA5A 72% 52% 35% 21% RQA5C 76% 55% 41% 24% RQA9A 49% 33% 23% 15% RQA9C 51% 40% 31% 20% DRX-1 RQA5A 38% 24% 12% 4% RQA5C 38% 25% 14% 5% RQA9A 28% 18% 9% 4% RQA9C 28% 19% 12% 5% * DQE values at the zero-frequency axis were estimated by the intercept of a linear fit of low-frequency data but excluding most proximal to the axis due to large fluctuations. Other estimated values are grouped into frequency bins due to the noisiness of the data. 22

36 considerable differences in the spatial resolutions of the detectors, as expected. The noise responses for each filtration were also similar, except at the lower frequencies of the NNPS especially near the zero-frequency axis. There, observing the NNPS responses at RQA5 for Pixium 4600 and DRX-1C in Figure 8, the NNPS for the IEC-based filtration (solid lines) tend to drop faster than the NNPS for the alternative filtration. This subsequently appears as a drop in DQE near the zero-frequency axis, shown for those detectors in Figure 10. Overall, as indicated in Table 5, the DQEs of the two filtrations, while similar in trend, indicate that the alternative filtration increases the DQE by a small amount of 3%-5%. Part of this may be explained by the slightly higher beam energy, which may be more optimal for the energy response of the detectors or may weigh the pixel responses slightly considering that they are energy-integrating types. The most probable explanation is the gain map correction for the alternative filtration, where fixed pattern noise is more sufficiently reduced. A previous study [6] had discussed the choice of filter material in the analysis of DQE when achieving the beam conditions defined by IEC. It found that visible nonuniformities were present with the higher purity aluminum filter (type alloy). The low frequency mottle in the flat-field images for NPS measurements were also attributed to structured noise from the grain size in the IEC-based filter, with an attenuating thickness that would reveal nonuniformities. The mottle in the current study was only observable under very narrow windowing, as shown in Figure 11. Such low 23

37 frequency artifacts, which are not readily noticeable, may also be caused by "shading" artifacts, inverse square law, or even the heel effect. A possible method to correct for this is a subtraction method by taking the average of the flat-field images for an exposure level and then subtracting that from each of them. This would remove nonuniformities that were not corrected using a suboptimal gain map calibration. Figure 11: DRX1-C NNPS images at 1 mr for RQA5 with IEC filtration (left) and alternative filtration (right). Images are equally windowed at 45 and leveled at 980. One convenient aspect of the copper and aluminum filtration is that it requires much less tube current to achieve the same amount of exposure at the detector than the much thicker aluminum filtration. As shown in the non-normalized spectra in Figure 2, the exiting photon fluence exiting the copper and aluminum filtration is substantially higher than that of the IEC-specified filtration. This is due to the smaller total filtration 24

38 attenuation. For extensive DQE analysis, multiple sets of exposures may be acquired before tube overheating becomes a concern. One limitation to the comparison of the two filtrations is that calibration procedures specified copper and aluminum filtration at 80 kvp (for all detectors 0.5 mm Cu and 1.0 mm Al). This may have influenced the results in favor of the alternative filtration. A further investigation involving the calibration procedures and performing DQE measurements is encouraged. Another factor may be influenced by the fact that the tests were performed at 70 kvp and 120 kvp, different from the recommended calibration tube potential. Clearly, there would be differences in the linear attenuation coefficients of the filters and different energy responses of the detectors themselves. This must be considered when interpreting DQE results. The current results support a previous study, decades ago, that described filtration of different material types in terms of an aluminum equivalent [16]. The results show that the two filtration schemes are essentially equivalent when considering beam qualities and spatial resolutions. The NNPS and DQE results can be seen as "close enough," where their small differences are insignificant when performing quality assurance tests in a clinical setting. Overall, our results indicate that the alternative filtration with copper and aluminum may be more convenient to use than the current IEC standard filtration. 25

39 I.4.iii. Implications of Wireless DR This study has shown that wireless image receptors can have the same DQE performance, if not better, than conventional flat-panel detectors. They operate on the same basic physical principles; the new features offered by the DRX-1C and DRX-1 are wireless communication with the workstation and electronics packaging technology. The latter feature may pose limitations for these units in terms of possible degradation in the detectors in routine clinical conditions. A consideration for future work would be to longitudinally track DQE performance of the wireless detectors over time while being utilized in a clinical environment. In the end, one must consider risks versus benefits of choosing portable DR technology over CR, one of which includes the cost and fragility of DR detectors. The DQE performance of one wireless system is just as good as or better than conventional systems, as seen by the DRX-1C performance compared to the Pixium Wireless systems can also reduce the need for CR readers, especially in portable applications in other regions of the world (e.g., military hospitals, developing countries). However, while DQE performance indicates the physical performance of the detector system, it is still unknown how it relates to observer performance. I.5 Conclusions Two wireless image receptors, DRX-1C and DRX-1, were evaluated and compared with the conventional DR flat-panel Pixium 4600 in terms of DQE 26

40 performance, along with MTF and NNPS performances. The detectors have similar resolution properties, although the DRX-1 is inferior at higher spatial frequencies. The NNPS and DQE results both indicate that the DRX-1C is superior to the DRX-1 and comparable, if not better, to the Pixium The results from the filtration comparison indicate no substantial differences between the IEC-based filtration and the copper-based alternative filtration. Only slight differences were found in the low frequency components of the NNPS and the DQE due to the inherent nonuniformities of the IEC specified filtration. Given the similarity of the results and low attenuation advantage of the copper and aluminum filter, its use is encouraged. 27

41 II. Directional MTF for Breast Tomosynthesis II.1 Introduction Breast tomosynthesis is an emerging 3D imaging modality that has potential use for screening and diagnosis of breast cancer. Breast tomosynthesis, along with other 3D techniques, is preferable to planar imaging methods (e.g., mammography) because they reduce anatomical noise by removing overlying structures above and below the plane of an image slice [17-20]. Recent advances in detectors and computer technology have made digital tomosynthesis feasible. An image quality metric of particular importance in breast tomosynthesis is spatial resolution. Resolution is important to know in order to assess small-detail structures such as microcalcifications. A descriptive metric for characterizing spatial resolution, in the Fourier (or frequency) domain, is the modulation transfer function (MTF). Affected by reconstruction filters [21], the limited angular projections involved in breast tomosynthesis results in highly anisotropic (or nonuniform) resolution. Many studies have looked only at characterizing the in-plane spatial resolution (i.e., in an individual slice) with an elevated angled edge phantom [22,23]. A few studies have looked at characterizing a more comprehensive 3D spatial resolution by using a phantom with angled wires or tubes [24-26]. However, such studies require precise mechanical alignment of the phantoms. Several studies have explored a method using a 28

42 sphere phantom for the directional 3D MTF evaluation for microtomography [27] and multi-slice CT [28,29]. This method has not yet been extended to breast tomosynthesis. This chapter focuses on breast tomosynthesis because it is highly anisotropic in spatial resolution and, like its predecessor mammography, requires high spatial resolution. Additionally, breast tomosynthesis acquisitions and reconstructions produce several types of artifacts. The use of a cone-based method using a sphere phantom [28] is explored to characterize the directional 3D spatial resolution of simulated images from breast tomosynthesis. A technique for removing out-of-plane artifacts of the ESFs for the in-plane axes is investigated to yield a modified MTF, in a method that separates artifact information from resolution information. II.2 Materials and Methods II.2.i. Image Simulation Breast tomosynthesis images were simulated by using a virtual imaging system, depicted in Figure 12. A volumetric breast phantom was voxelized as a rectangular mass of uniform breast equivalent tissue of 4 cm thickness embedded with fifteen evenly spaced plastic sphere inserts of 12 mm diameter. The spheres were placed in a grid formation within the central plane of the phantom. The x-ray fluence was modeled from a 28 kvp beam incident upon an indirect flat-panel detector with 200 µ m pixel size. Twenty-three projections within an angular range of 44 were simulated using cascaded systems analysis to generate characteristic 2D noise and spatial blurring [29]. Each 29

43 projection was simulated to have an exposure of 17.4 mr with a fluence of photons mm -2. A standard filtered backprojection technique based on the Feldkamp reconstruction algorithm [29] was used to reconstruct the projections and produce a volumetric dataset with an isotropic voxel size of 200 µ m. Figure 12: Depiction of the virtual image system. II.2.ii. Uncorrected MTF To enable comparison of multiple spheres, the reconstructed volume was initially homogenized by performing a background subtraction based on a portion of the volume devoid of spheres. The voxel values were rescaled between one and zero to eliminate negative values. 30

44 The volumetric data were segmented to extract individual regions of interest (ROIs) each containing a single sphere. The ROIs extended along the full range of the z- axis. A thresholded ROI was generated by determining the exterior and interior voxels relative to the sphere in the ROI. The threshold value was set at 45% of the maximum voxel value prior to thresholding. The exterior and interior voxel values were then set to values of 0 and 1, respectively. Using the thresholded volume, the center of mass was calculated to determine the centroid. The voxel values from the original ROI were subsequently tabulated with the associated distances, azimuthal angles, and polar angles relative to the centroid. Conical regions were prescribed along the positive and negative directions along the three major axes extending from the centroid of the sphere, as depicted in Figure 13. The axes, about which the extent of the cone angle was delineated, were defined with the azimuthal and polar angles. Voxels with centers within the angular range of the cone were considered for generating the edge spread function (ESF). To improve regularity of the distance sampling interval, the ESF values were rebinned to discrete distances corresponding to a fraction of the voxel size. Only voxels with distances ranging from the voxel size (i.e., 200 µ m) to the maximum distance were considered. The ESFs from multiple spheres were averaged together for each of the three major axes to produce an averaged ESF, which was further smoothed utilizing a Gaussian filter. 31

45 Figure 13: Example of 30-degree cone prescribed along z axis of the sphere. The resulting ESF was then differentiated using the central difference method to produce the line spread function (LSF). A Hanning filter with the same length as the LSF was applied to zero out the tails of the LSF. The presampled MTF was subsequently computed as the amplitude of the Fourier transform of the LSF. The MTF was normalized with respect to the maximum value occurring within the range of the cutoff frequency. Binning size and conical range for the ESF were considered for maximizing accuracy and minimizing noise of the MTF, verified by comparison against the theoretical MTF as determined in the previous section. II.2.iii. Theoretical Directional MTF The theoretical 3D MTF was calculated using a priori knowledge of the transfer function of the virtual imaging system described in the previous section. A phantom was created with a set of point objects in a uniform and noise-free background with the objects spanning across the volume of the breast [29]. Twenty-one realizations were 32

46 generated from the reconstructed images of the point objects to yield a set of 3D point spread functions (PSFs). The 3D fast Fourier transform (FFT) was performed for each 3D PSF and averaged to give an expectation 3D MTF [29]. The theoretical directional MTFs in the three major spatial axes were determined by line profiles along each of the corresponding spatial frequency axes in the 3D MTF. An additional theoretical MTF for each direction was determined by using the application of conical regions along the axes in frequency-space to take into account the contributions of MTF information from other planes. II.2.iv. Modified MTF The tomosynthesis reconstruction is known to have edge enhancements, which affect the overall MTF by shifting the peaks of the MTF toward the higher frequencies [23]. The presence of this artifact complicates the interpretation of the actual spatial resolution of the images. Several steps were performed to remove the artifact contribution to the resolution information, particularly for the in-plane x and y directions, with the assumption that resolution information was contained immediately near the edge. For the x-direction averaged ESF, only values that were detected to be inside the edge of the sphere were considered. Those values were previously determined via thresholding for calculating the centroid. The ESF information corresponding to these values was inversed and flipped about the detected edge to produce a symmetric 33

47 modified ESF. The modified MTF was subsequently calculated from this modified ESF as described in the previous section. For the y-direction averaged ESF, an upward trend was found in the initial part of the ESF. This section was detrended with a polynomial fit and subtracted to produce a flatter curve in that region. The resulting detrended ESF was used to calculate the y axis modified MTF. Figure 14: Photograph of the imaging system with the acrylic sphere phantom embedded in oil. II.2.v. Preliminary Experimental Validation A clinical breast tomosynthesis system (Mammomat Inspiration, Siemens AG, Munich, Germany) was used to perform a preliminary evaluation of the cone-based MTF technique. The phantom for the experiment consisted of a single acrylic ball of 0.75 in diameter (SmallParts, Seattle, WA) suspended by a in diameter plastic filament 34

48 (Omniflex, Zebco, Tulsa, OK) in an acrylic frame filled up to 4 in with vegetable oil (Target Brands, Inc., Minneapolis, MN). The system and phantom are shown in Figure 14. Twenty-five projections with an angular range of 44 were acquired and subsequently reconstructed to produce a volume with a voxel size of mm 3. The voxels were reformatted to have an isotropic size of 0.1 mm. The uncorrected ESF, LSF, and MTF were calculated as described in the previous section. II.3 Results II.3.i. Reconstruction The reconstructed volume is shown in Figure 15. Notice the edge enhancement along the x-direction, as indicated by the sharp shadowing artifacts on either side of the spheres. The background was effectively homogenized using the background subtraction technique. This also took account of the curved edges of the breast phantom. With the close spacing of the spheres in the phantom, the shadows along the x direction for the fifteen spheres overlap with each other. As the nine centrally located spheres experience this effect the same way, they were used for determining the ESF. A 3D rendering of the ROI containing a sphere, shown in Figure 16, indicates the anisotropic resolution of the reconstruction. Note that the sphere is not accurately reconstructed and has an oblong shape, especially along the z axis. Cross sectional views of the ROI, also in Figure 16, clearly demonstrate the edge enhancement causing a shadow artifact in the x direction caused by the incomplete angular sampling of 35

49 tomosynthesis. The sampling also introduces the triangular reconstruction of the sphere as seen in the x-z plane. Note the gradual edge drop-off in the z direction much beyond the sphere radius. Figure 15: View of the central slice of the breast phantom reconstruction before (top) and after (bottom) background subtraction. The z axis is through the page. 36

50 Figure 16: 3D rendering of the ROI volume (left) and cross-sectional views of the most centrally located sphere with centroid indicated with red circle (right). II.3.ii. Theoretical MTF The theoretical MTFs for x, y, and z directions as determined from the line profiles of the 3D MTF are shown in Figure 17. The theoretical MTF in the x direction has a maximum value that is toward higher frequencies. Its 10% response occurs at about 1.25 cycles/mm, which is at 50% of the cutoff frequency. The rapid increase from the zero-frequency intercept to the peak corresponds to the ramp filter used in filtered backprojection, which decreases the weighting of low frequency contributions due to the incomplete angular sampling of the frequency-space. The MTF does not reach a value of 0 at the zero-frequency intercept as it is very difficult to assess the zero-frequency intercept due to the finite size of the phantom. The theoretical MTF in the y direction peaks at the zero-frequency intercept and reaches 20% proximal to the cutoff frequency. 37

51 The 10% MTF is well beyond the cutoff frequency. The theoretical MTF in the z direction has a rapid drop-off at very low spatial frequencies, indicating the lack of resolution in that dimension. Figure 17: Theoretical 3D MTF results along the three major planes (top) and along x, y, and z directions (bottom). Also note that the angular spread seen in the fx-fz plane is equal to the angular range of 44 for the acquisition. II.3.iii. Uncorrected MTF The ESF, LSF, and MTF using the cone-based method are shown for the x, y, and z directions in Figure 18. It was found that a bin size of one-tenth the voxel size (0.02 mm) and a cone angle of 30 to establish the ESF were enough to minimize noise and maximize accuracy in the uncorrected MTFs, considering the reasonable comparison of the shapes of the MTF curves with the theoretical results in Figure 17. The LSFs are generally noisy because differentiation of the ESF increases the amplitude of the noise. 38

52 The data shown reflect a convolution with a smoothing Gaussian filter, which was later further corrected for in the reported MTF. Nevertheless, the high frequency components of the noise are well beyond the MTF cutoff frequency of 2.5 cycles/mm and do not impact the MTF results greatly. For the ESF in the x direction, the shadow effect evident at the edge of the sphere is visible as a steep decline followed by an increase. Due to the finite distance range provided by the ROI, the ESF beyond the edge did not asymptotically reach the background value. The corresponding LSF demonstrates a low frequency modulation that is indicated by the shift of 0.3 cycles/mm in the x direction for the peak of the MTF. The MTF exhibits a zero-frequency intercept that is non-zero, unlike the theoretical MTF, and a 10% value at approximately 1 cycles/mm. These features may be a direct consequence of MTF information contamination from y and z directions. Furthermore, the ESF in the y direction demonstrates a reasonably shaped curve except for the slight upward trend within the radius of the sphere, which can be attributed to the shadow artifact overlapping with the sphere volume. The associated MTF has a peak shifted by approximately 0.1 cycles/mm away from the axis and a 10% MTF occurring at approximately 1.5 cycles/mm. Both features, which are not present in the theoretical results, may also be attributed to contaminant MTF information from x and z directions. The ESF in the z direction has a drop-off that occurs at a small fraction of the cutoff frequency, similar to that demonstrated by the theoretical MTF. 39

53 Uncorrected ESF, LSF, and MTF Figure 18: Uncorrected ESF (top), LSF (middle), and MTF (bottom) for x, y, and z directions. 40

54 Figure 19: Comparisons of the directional MTFs as calculated by the sphere method (dashed line), by theoretical line profiles (light-weight line), by theoretical cone regions (heavy-weight line). II.3.iv. Comparison of Theoretical and Simulated MTFs The theoretical MTF results obtained from line profiles through the 3D MTF and the simulated MTFs using the cone-based technique did not match very well, except for the general shape of the curves. It was assumed in the previous section that the conebased technique contains information from other planes. Figure 19 compares MTFs in each direction for the two methods described in the methods and an additional method based on conical regions of the 3D MTF. The latter computes the MTF by averaging contributions of the 3D MTF using the same cone prescription method used to define the ESFs. Comparison of the curves indicate some interesting correlations, aside from the fact that using conical regions with the 3D MTF results produce more noisy MTF results, partly due to the low sampling provided by the theoretical calculations. The same conclusions regarding the z direction MTF can be confirmed regardless of either theoretical MTF procedures. The experimental x direction MTF seems to agree best with 41

55 the line profile method whereas the y direction MTF agrees better with the cone region method. The fact that the experimental x direction MTF has a drop-off frequency that is lower than those of either of the theoretical MTFs in Figure 19 suggests that this might be due to integration of the z-direction in the in-plane slices, considering how slices are essentially averages of z direction information contained within it [33]. II.3.v. Modified MTF for x and y Modified ESF, LSF, and MTF curves for x and y directions are shown in Figure 20. The modified ESF and the resulting LSF in the x direction appear symmetric, as expected from the inverse and flip operation of the interior ESF about the detected edge. The modified MTF appears with less variation than the uncorrected MTF, and the MTF peak occurs at the zero-frequency axis. The correction yields a 10% MTF at about 1.5 cycles/mm, an improvement from the uncorrected MTF but still distant from the cutoff frequency. The modified ESF in the y direction demonstrates the detrended curve within the sphere radius after a quadratic polynomial fit. The resulting modified MTF still appears similar to the uncorrected MTF, except that the peak now coincides with the zero-frequency axis. For both x and y directions, the low response of the modified MTFs at the higher frequencies suggests that the contamination from other directions is substantial due to the angular range of the cone. 42

56 Modified ESF, LSF, and MTF Figure 20: Modified ESF (top), LSF (middle), and MTF (bottom) for x and y directions. 43

57 II.3.v. Preliminary Experimental Validation Cross-sections of the reconstructed sphere volume are shown in Figure 21. Relative to the simulation reconstructions, the reconstructions of the experimental phantom images produce lower contrast and higher noise. The preliminary results, shown in Figure 22, indicate that our technique can be applied to actual experimental breast tomosynthesis reconstructions. However, due to the noise exhibited by the MTF curves for the x and y directions, we did not determine the modified MTFs to separate resolution and artifact information. Figure 21: Cross sectional views of the experimental sphere image with centroid indicated with red circle. 44