ABSTRACT 1. INTRODUCTION

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1 Gaussian frequency blending algorithm with Matrix Inversion Tomosynthesis (MITS) and iltered Back Projection (BP) for better digital breast tomosynthesis reconstruction Ying Chen a,b, Joseph Y. Lo a,b,c,d, Jay A. Baker b,c, James T. Dobbins III a,b,c,d a Department of Biomedical Engineering, Duke University, Durham, NC, USA b Duke Advanced Imaging Laboratories, Duke University Medical Center, Durham, NC, USA c Department of Radiology, Duke University Medical Center, Durham, NC, USA d Medical Physics Graduate Program, Duke University Medical Center, Durham, NC, USA ABSTRACT Breast cancer is a major problem and the most common cancer among women. The nature of conventional mammography makes it very difficult to distinguish a cancer from overlying breast tissues. Digital Tomosynthesis refers to a three-dimensional imaging technique that allows reconstruction of an arbitrary set of planes in the breast from limited-angle series of projection images as the x-ray source moves. Several tomosynthesis algorithms have been proposed, including Matrix Inversion Tomosynthesis (MITS) and iltered Back Projection (BP) that have been investigated in our lab. MITS shows better high frequency response in removing out-of-plane blur, while BP shows better low frequency noise prosperities. This paper presents an effort to combine MITS and BP for better breast tomosynthesis reconstruction. A high-pass Gaussian filter was designed and applied to three-slice slabbing MITS reconstructions. A low-pass Gaussian filter was designed and applied to the BP reconstructions. A frequency weighting parameter was studied to blend the high-passed MITS with low-passed BP frequency components. our different reconstruction methods were investigated and compared with human subject images: 1) MITS blended with Shift-And-Add (SAA), 2) BP alone, 3) BP with applied Hamming and Gaussian ilters, and 4) Gaussian requency Blending (GB) of MITS and BP. Results showed that, compared with BP, Gaussian requency Blending (GB) has better performance for high frequency content such as better reconstruction of micro-calcifications and removal of high frequency noise. Compared with MITS, GB showed more low frequency breast tissue content. Keywords: mammography, tomosynthesis, Gaussian requency Blending (GB), shift-add-add (SAA), filtered back projection (BP), matrix inversion tomosynthesis (MITS) 1. INTRODUCTION Over the last two decades, breast imaging has dramatically changed. It is universally accepted that mammography is the most important and efficacious tool for the early detection of breast cancer [21]. However, limitations of mammography have been well publicized, such as 20% false negative rate [22, 23], many callbacks from screening, and low positive predictive value of about 15-34% from biopsy [24, 25]. About 30% of breast cancers are still missed in traditional mammography [20]. The nature of the two-dimensional mammography makes it very difficult to distinguish a cancer from overlying breast tissues, and the interpretation can be variable among radiologists. Meanwhile, it is particularly difficult for mammography to interpret dense breast tissues, which is common in young women. Digital tomosynthesis is a promising technique for clinical mammographic application. Digital Tomosynthesis refers to a three-dimensional imaging technique that allows reconstruction of an arbitrary set of planes in the breast from limitedangle series of projection images as the x-ray source moves. Compared with traditional two-dimensional Medical Imaging 2006: Physics of Medical Imaging, edited by Michael J. lynn, Jiang Hsieh, Proceedings of SPIE Vol. 6142, 61420E, (2006) /06/$15 doi: / Proc. of SPIE Vol E-1

2 mammography, tomosynthesis imaging methods can provide three-dimensional reconstruction slices. This can improve conspicuity of structures by removing the visual clutter associated with overlying anatomy [1, 2, 3, 4, 11, 12]. In the field of breast tomosynthesis imaging, investigations of various techniques have been undertaken by several research groups, including Shift-And-Add (SAA) [1,2,3], Niklason and colleagues publication in 1997 of a tomosynthesis method with the x-ray tube moved in an arc above the stationary breast and detector [11], Wu et al. s report in 2003 of the maximum likelihood iterative algorithm (MLEM) to reconstruct the three-dimensional distribution of x-ray attenuation in the breast [12], and the filtered back projection (BP) algorithms from Stevens et al. [15], Lauritsch et al. [16], and Matsuo et al. [17]. In the end of 2004, we also reported the application of the Matrix inversion tomosynthesis (MITS) technique in breast tomosynthesis [3]. In early 2005, we reported the impulse response analysis with several different tomosynthesis reconstruction algorithms, including the comparison of SAA, NIKL, BP, and MITS algorithms [2]. Among the above tomosynthesis reconstruction algorithms, MLEM is the slowest reconstruction method due to its iterative mathematical nature. Compared with SAA and NIKL, MITS and BP use deblurring functions and provided better removal of out-of-plane blur. Initial investigations have shown that MITS and BP are capable of reconstructing slice images throughout the breast to provide three-dimensional information [2, 3, 4]. MITS has better performance for high frequency content while BP has better reconstructions for low frequency content. This paper is an effort to investigate a frequency blending method by correctly blending the low frequency part of BP and high frequency part of MITS together for a fast and better breast tomosynthesis reconstruction algorithm. 2. METHODS our different reconstruction methods were investigated and compared with human subject images: 1) Matrix Inversion Tomosynthesis (MITS) blended with Shift-And-Add (SAA), 2) iltered Back Projection (BP) alone, 3) iltered Back Projection (BP) with applied Hamming and Gaussian ilters, and 4) Gaussian requency Blending (GB) of MITS and BP. 2.1 MITS blended with SAA Linear algebra was used in the MITS algorithm to enable fast reconstruction of arbitrary planes with a deblurring method to solve for the blurring function in each reconstructed plane [1,2,4-10]. In the spatial domain, the conventional shift-and-add tomosynthesis of n reconstructed planes can be represented as the convolution of the actual in-plane structures s and the blurring function f relating how structures residing in one plane are reconstructed in another: t = s + s + + s t. t 1 2 n 1 = s 1 = s n1 2 + s + s n2 n + + s n + + s n 1n The above convolution can be expressed in ourier frequency space: 2n nn (1) T1 T2 = Tn n n2 1n 2n nn S1 S 2 S n (2) Proc. of SPIE Vol E-2

3 Equation (2) can also be written as: T = M S, where M is the matrix of the ourier Transform of blurring functions, 1 1 and S is the matrix of ourier Transform of the real structures. Thus, one has s = T ( M T ) to solve the real structures s. The application of the Matrix inversion tomosynthesis (MITS) technique in breast tomosynthesis was reported by our lab in the end of 2004 [3]. Results showed that MITS matrix inversion demonstrates excellent rendition of mid- and high-frequencies. However, due to poor matrix conditioning at the lowest spatial frequencies, the MITS algorithm needs to be improved for the lowest frequency contents. In order to get better reconstruction for low frequency content, a frequency blending method was applied to combine the frequency contents of MITS and SAA reconstruction images in our lab. In order to control noise and artifacts, a technique named Slabbing combing adjacent planes with a sliding average was investigated in our lab originally for pulmonary nodule detection with the MITS algorithm. Here we used the same technique for breast tomosynthesis imaging and five-slice Slabbing method was applied to the MITS reconstruction of the breast. 2.2 iltered Back Projection (BP) iltered back projection (BP) algorithms are used widely in computed tomography (CT). or tomosynthesis reconstruction, based on the central slice theorem, a parallel projection samples the object on a plane perpendicular to the projection plane. In frequency space, the main limitation of the tomosynthesis reconstruction is the incomplete sampling. or the breast tomosynthesis reconstruction, we designed a BP algorithm based on the central slice theorem and ourier frequency sampling density. A specific inverse filter was designed based on the sampling density, which is calculated as the inverse of the shortest distance from a sampled point in ourier space to sampled points from another view [2,15,16,19]. 2.3 BP with applied Hamming filter and Gaussian ilter In order to control the high frequency noise amplification typical of BP, specific Hamming Gaussian filters were designed and applied to our BP algorithm. Results showed that the Hamming filter and Gaussian filter were effective at suppressing high frequency noise [2]. Different parameters were investigated for applied Hamming filter and Gaussian filter to control high frequency noise 2π i while maintain good low frequency content. The applied Hamming filter is: w( i) = *cos( ), where i N is the individual frequency bin out of N total frequency bins in frequency space. or these investigations, images were subsampled down to a size of 1024 * 1024, yielding N=2048 frequency bins. Groups of reconstructions from different parameters of 0.2, 0.5, 0.54, 0.8 were compared. As a compromise for less aggressive filtering while maintaining good reconstruction results, the parameter 0.5 was chosen. 2 2 The Gaussian filter used is: G( i) = exp( i / k ), where i is the individual frequency bin in frequency space and k is the kernel size. Different reconstructions from different kernel sizes were compared. Among them, k=300 was chosen as a good compromise between noise suppression and spatial resolution 2.4 Gaussian requency Blending (GB) of MITS and BP Initial studies showed that MITS and BP are capable of reconstructing three-dimensional breast images to provide depth information in the subject. Preliminary human subject experiments demonstrate that MITS has better performance for high frequency solution, while BP has better reconstructions for low frequency content. Both tomosynthesis algorithms have their advantages and disadvantages as well. Proc. of SPIE Vol E-3

4 In order to combine advantages of MITS and BP together to generate better reconstruction images, a Gaussian requency Blending (GB) method was investigated. or this algorithm, we applied a high-pass Gaussian filter to the three-slice slabbing MITS reconstructions, and a low-pass Gaussian filter to the BP reconstructions. As described in 2.1, slabbing technique can control noise and artifacts on MITS reconstruction images. Here, three-slice slabbing technique was applied to MITS reconstruction images for the preparation for our GB method. As described in 2.2, BP reconstructions were also done to provide the basis of good low frequency content. Briefly speaking: GB= (High Pass MITS) + weighting-factor *(Low Pass BP). Before the application of GB, gains and offsets of both MITS and BP algorithms were matched. Projection images of a two-dimensional square located at 33.5mm above the detector surface were simulated and reconstructed. The air gap distance of our tomosynthesis system is 15.5mm. According to the profiles of reconstructed square images, gains and offsets were matched. The noise power spectra of the reconstruction plane at 33.5mm above the detector surface were investigated for consideration of selecting optimal parameters based on the noise characteristics of both MITS and BP algorithms. A tomosynthesis sequence of flat images with acquisition technique of 25 projections and ±25 0 angular range was acquired by Siemens full-field digital mammographic system with pixel resolution of 85 µm (selenium-based direct conversion Siemens Mammomat Novation prototype system). Non-normalized NPS estimates were generated using 64 ROIs of size 128*128 according to our previously published methods [20]. Noise power spectra from different kernel sizes of the GB filter and weighting factors were investigated. After that, reconstruction images of a human subject were studied subjectively to determine the optimal parameters. The kernel size of 140 and the frequency-weight of 0.1 were chosen to correctly match the frequency components from MITS and BP. 3. RESULTS AND DISCUSSION The plot of applied Gaussian Blending filters with kernel size of cycles/mm (140 frequency bins) was shown in figure 1. igure 2, 3, 4 show that noise power spectra of MITS, BP and GB with weighting factor of 0.1 and kernel sizes of 80, 140, 200 frequency bins (each frequency bin is cycles/mm). Gaussian nequenny Blending lillens Kennel Gize=0.4O2lnynles/mm (140 lneq bins) MITS BP 0 GB Hgh ess GB Inn MITO E 10 ( L wp GBO BP C cycles/mm igure 1: Gaussian requency Blending filters cycle/mm igure 2: NPS with kernel=80, weighting=0.1 Proc. of SPIE Vol E-4

5 MITS BP GB 10 igure 3: NPS: kernel=140, weighting=0.1 igure 4: NPS: kernel=200, weighting=0.1 rom figure 2, 3, 4, we find that when the kernel size of the Gaussian Blending filters increases, the NPS curve of GB will be more apart from the MITS curve, since more low-to-middle frequency content from BP are used for blending. This will bring high frequency noise to the blended reconstruction images because BP has worse high frequency solution. However, if narrower kernel size is used, more middle-to-high frequency contents from MITS will be included in blending. Blur artifacts of the low frequency contents will occur because of MITS s relative poor solution for low frequency contents. The weighting factor plays a similar role. If the weighting factor is too big, BP components will be enlarged while MITS components will be suppressed. If the weighting factor is too small, the opposite problem will occur. Thus, according to the reconstruction images from a human subject, we subjectively selected kernel size of 140 and weighting factor of 0.1 as our optimal parameters for GB. igure 5 shows reconstructed ROI images of micro-calcifications of a human subject. igure 6 shows the same reconstruction planes with those micro-calcifications on them. (a) (b) (c) (d) are from above four different reconstruction algorithms: MITS, BP without Hamming and Gaussian filters, BP with Hamming filter and Gaussian filter, and GB of MITS and BP. igure 5: Reconstructed ROI of micro-calcifications: (a) MITS (b) BP without Hamming ilter and Gaussian ilter (c) BP with Hamming ilter and Gaussian ilter (d) Gaussian requency Blending (GB) of MITS and BP (a) (b) (c) (d) We found that the MITS showed good high frequency reconstructions for micro-calcifications in igure 5(a), but the low frequency content of the breast tissue was less obvious compared with others in igure 6(a). In igure 5 (b), BP had worse high frequency noise compared with MITS, but showed better performance for low frequency components in igure 6(b). After applying the Hamming ilter and Gaussian ilter, the BP with Hamming ilter and Gaussian ilter in igure 5(c) and igure 6(c) reduced high frequency noise and provided better reconstructions than BP only. Proc. of SPIE Vol E-5

6 However, the margins of the micro-calcifications were worse due to the applied low pass Hamming ilter and Gaussian ilter. igure 5(d) and 6(d) show the GB of MITS and BP. Compared with MITS, the GB has improved low frequency content from BP for clear breast tissue and vessel background, and yet better high-frequency noise properties than BP alone. Compared with BP, GB provided better high frequency contents for micro-calcifications with clear edges and less noise. 4. CONCLUSION rom a few human subject studies, we found that MITS showed good high-frequency reconstructions especially for micro-calcifications. BP has better low frequency solution. BP with Hamming ilter and Gaussian ilter greatly reduced the high frequency noise, while at the expense of introducing blur to the margins of the micro-calcifications. Gaussian requency Blending (GB) of MITS and BP retains the good low-frequency solution of BP, and keeps the good performance for high-frequency content from MITS. Compared with MITS, the GB has improved low frequency response from BP for clear breast tissue and vessel background. Compared with BP, GB provided better high frequency content for clear margins of micro-calcifications with less noise. igure 6(a): MITS Proc. of SPIE Vol E-6

7 igure 6(b): BP without Hamming ilter and Gaussian ilter igure 6(c): BP with Hamming ilter and Gaussian ilter Proc. of SPIE Vol E-7

8 igure 6(d): Gaussian requency Blending (GB) of MITS and BP ACKNOWLEDGMENTS This work was supported in part by a research grant from Siemens. REERENCE 1. James T. Dobbins, III., Devon J. Godfrey, Digital X-ray tomosynthesis: current state of the art and clinical potential, Phys. Med. Biol. 48: R65-R106, Ying Chen, Joseph Y. Lo, James T. Dobbins III, Impulse response analysis for several digital tomosynthesis mammography reconstruction algorithms, Proc. SPIE, Volume 5745, Physics of Medical Imaging, pp , Ying Chen, Joseph Lo, James T. Dobbins III, Matrix Inversion Tomosynthesis (MITS) of the Breast: Preliminary Results, RSNA 90 th Scientific Assembly, Chicago, IL, Michel Bissonnette, Marc Hansroul, Eric Masson, Serge Savard, Sébastien Cadieux, Patrick Warmoes, Daniel Gravel, Jerry Agopyan, Brad T. Polischuk, Wolfgang H. Haerer, Thomas Mertelmeier, Joseph Y. Lo, Ying Chen, James T. Dobbins III, Jonathan L. Jesneck, Swatee Singh, Digital breast tomosynthesis using an amorphous selenium flat panel detector, Proc. SPIE, Volume 5745, Physics of Medical Imaging, pp , J. T. Dobbins, III., A. O. Powell, and Y. K. Weaver, Matrix inversion tomosynthesis: Initial image reconstructions, Abstract Summaries of the RSNA, 165(P), pp. 333, J. T. Dobbins, III., Matrix Inversion Tomosynthesis improvements in longitudinal x-ray slice imaging, U.S. Patent #4,903,204 (1990). Assignee: Duke University. Proc. of SPIE Vol E-8

9 7. R. J. Warp, D. J. Godfrey, J. T. Dobbins, III., Applications of matrix inverse tomosynthesis, Proc. SPIE, Volume 3977, Physics of Medical Imaging, 1(22): , D. J. Godfrey, R. L. Warp, J. T. Dobbins, III., Optimization of matrix inverse tomosynthesis, Proc. SPIE, Volume 4320, Physics of Medical Imaging, 2(25), pp , D. J. Godfrey, A. Rader, J. T. Dobbins III, Practical strategies for the clinical implementation of matrix inversion tomosynthesis, Proc. SPIE, Volume 5030, Physics of Medical Imaging, D. J. Godfrey and J. T. Dobbins III, Optimization of matrix inversion tomosynthesis via impulse response simulations, RSNA 88 th Scientific Assembly, Chicago, IL Loren T. Niklason, et al., Digital tomosynthesis in breast imaging, Radiology 205: , Tao Wu, et al., Tomographic mammography using a limited number of low-dose cone-beam projection images, Med. Phys. 30 (3): , March B. G. Ziedses des Plantes, Eine neue methode zur differenzierung in der roentgenographie (planigraphie). Acta Radiologica, 13: , D. G. Grant, Tomosynthesis: a three-dimensional radiographic imaging technique, IEEE Transactions on Biomedical Engineering. BME-19: 20-28, Grant M. Stevens, Rebecca ahrig and Norbert J. Pelc, iltered backprojection for modifying the impulse response of circular tomosynthesis, Med. Phys. 28: , G. Lauritsch and W. Haerer, A theoretical framework for filtered back-projection in tomosynthesis, Proc. SPIE 3338: , Hiroshi Matsuo, Akira Iwata, Isao Horiba, Nobuo Suzumura, Three-dimensional image reconstruction by digital tomo-synthesis using inverse filtering, IEEE Trans. Med. Imaging. 12: , J. Duryea, J. T. Dobbins III, J. A. Lynch, Digital tomosynthesis of hand joints for arthritis assessment, Med. Phys. 30 (3): , March L. A. eldkamp, L. C. Davis, J. W. Kress, Practical come-beam algorithm, J. Opt. Soc. Am. A 1: , Tao Wu, R. H. Moore, E. A. Rafferty, D. B. Kopans, A comparison of reconstruction algorithms for breast tomosynthesis, Med. Phys. 9: , September Lawrence W. Bassett, Valerie P. Jackson, Karin L. u, Yao S. u, Diagnosis of Diseases of the Breast, 2 nd ed, Elsevier Saunders, Philadelphia, Pennsylvania, L. J. W. Burhenne, S. A. Wood, C. J. D Orsi, S. A. Eeig, D. B. Kopans, K.. O Shaughnessy, E. A. Sickles, L. Tabar, C. J. Vyborny, and R. A. Castellino, Potential contribution of computer-aided detection to the sensitivity of screening mammography, Radiology, 215: , H. C. Burrell, D. M. Sibbering, A. R. Wilson, S. E. Pinder, A. J. Evans, L. J. Yeoman, C. W. Elston, I. O. Ellis, R. W. Blamey, and J.. Tobertson, Screening interval breast cancers: mammographic features and prognosis factors, AJR, 199: , A. M. Knutzen, and J. J. Gisvold, Likelihood of malignant disease for various categories of mammographically detected, nonpalpable breast lesions, Mayo Clin Proc, 68: , D. B. Kopans, The positive predictive value of mammography, AJR, 158: , Proc. of SPIE Vol E-9

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