Detector Noise evaluation by means of Continue Wavelet Transform. Comparison with Fourier Transform methods

Transcription

1 Detector Noise evaluation by means of Continue Wavelet Transform. Comparison with Fourier Transform methods Poster No.: C-0215 Congress: ECR 2014 Type: Scientific Exhibit Authors: N. Kalyvas 1, S. Angelakis 1, A. Poulakis 2, S. Tsantis 1, C. Michail 1, Keywords: DOI: G. Fountos 1, I. Valais 1, I. Kandarakis 1 ; 1 Athens/GR, 2 Athesn/GR Radiation physics, Mammography, Experimental, Computer Applications-General, Equipment, Physics, Quality assurance /ecr2014/C-0215 Any information contained in this pdf file is automatically generated from digital material submitted to EPOS by third parties in the form of scientific presentations. References to any names, marks, products, or services of third parties or hypertext links to thirdparty sites or information are provided solely as a convenience to you and do not in any way constitute or imply ECR's endorsement, sponsorship or recommendation of the third party, information, product or service. ECR is not responsible for the content of these pages and does not make any representations regarding the content or accuracy of material in this file. As per copyright regulations, any unauthorised use of the material or parts thereof as well as commercial reproduction or multiple distribution by any traditional or electronically based reproduction/publication method ist strictly prohibited. You agree to defend, indemnify, and hold ECR harmless from and against any and all claims, damages, costs, and expenses, including attorneys' fees, arising from or related to your use of these pages. Please note: Links to movies, ppt slideshows and any other multimedia files are not available in the pdf version of presentations. Page 1 of 9

2 Aims and objectives Image detector noise evaluation is critical in diagnostic radiology since it enables the optimization in detector design and exposure parameters. Noise is measured either by calculating the standard deviation of a uniformly exposed image or the corresponding Noise Power Spectrum (NPS), defined as the Fourier Transform of the signal variations. The knowledge of the frequency depended NPS (Dobbins et al 2006) enables the calculation of other useful frequency depended parameters like Detective Quantum Efficiency (DQE), showing the effectiveness of the Signal-to-Noise ratio transfer in spatial frequency. Besides Fourier Transform, which only gives frequency related information, another transform widely used in image processing exist; the Wavelet Transform. The wavelet transform is a powerful tool for image evaluation since it provides both frequency and spatial information, which may lead to combined detector noise characterization. The aim of this work is the evaluation of noise images through continues wavelet transform (CWT) and associate the CWT parameters with traditional Fourier based methods. Methods and materials Fourier Transform The Fourier Transform analyses a signal in terms of spatial frequency, that is demonstrates the periodicity, or else how often, a certain "pattern" is appeared. In noise analysis, Fourier Transform shows the signal variations distribution per frequency bin. This is important for identifying noise sources with known frequency behavior and estimate the effect of noise in imaging details, which are usually observed in medium and high spatial frequencies (above 4lp/mm). Noise is evaluated through the NPS as follows. A uniformly X-ray exposed image is used and the signal variations per pixel are calculated and the result is Fourier Transformed. The square of the amplitude corresponds to NPS [Dobbins et al 2006]. Although this method provides frequency depended noise characteristics it does not depict the position of possible gross non uniformities. Wavelet Transform The Continues Wavelet Transform (CWT) is a powerful tool for frequency analysis [Kirby 2005]. It uses customary functions called wavelets, in the form Z(a, b, x) to be applied to a spatial signal S(x). a is the scale parameter showing how dilated (high or low frequency analysis) is the wavelet. b is a parameter showing the translation, i.e. the portion of S(x) is examined every time. The application of CWT can yield arithmetical values for the wavelet coefficients. A high value of the wavelet coefficient suggests high signal translations Page 2 of 9

3 from point to point. Having in mind that the smaller point is the pixel, high values of the coefficient theoretically suggests high frequency information. Measurement Methodology The GE IQST phantom was uniformly irradiated with a Rh/Rh anode/filter combination spectrum at 28kVp and 50mAs and the corresponding digital image, through the CsI:Tl detector was obtained. The pixel size was approximately 0.1mm. In addition, a Gd 2 O 2 S phosphor screen of 33mg/cm 2 surface density was prepared by sedimentation [Kalivas et al 2007] in our laboratory. This manufacturing technique although considered to produce uniform detectors it may produce material displacement at the manufacturing process thus local non uniformities. The phosphor screen was came in contact with a film and irradiated with a Mo/Mo spectrum at 28kV and 10mAs. The film image was digitized at 1000ppi. The digital detector as well as the phantom image is shown in Figure 1. In both images the signal variations per pixel were obtained by subtracting the mean pixel value by each pixel. A 2D CWT transform by using the wavelet of Morlet [Kirby 2005], with scale 2, was applied and the corresponding images of the wavelet coefficients are shown in Figure 2. Furthermore the NPS by means of the Fourier Transform methodology of the subtracted images were derived. Images for this section: Page 3 of 9

4 Fig. 1: Figure1: Images of the digital detector (a) and the phosphor screen (b) Page 4 of 9

5 Fig. 2: Figure 2: Application of the CWT to the digital detector (a) and the phosphor screen (b) Page 5 of 9

6 Results In Figure 3 the NPS via Fourier transform is demonstrated. It may be observed that the phosphor image having larger in-homogeneities, shows more low frequency noise components. In Figure 4 the histogram of the wavelet coefficients values, derived from figures 2 are demonstrated. It may be observed that the phosphor screen wavelet coefficients present lower values than the digital detector wavelet coefficients. Since te exposure conditions of the two experiments were not the same and the evaluation of the zero frequency NPS could be misleading, the Noise Transfer Function was calculated as the square root of NPS normalized to zero frequency. NTF is shown to Figure 5. It is observed from Figure 5 that the digital detector shows higher noise components per frequency specially for high spatial frequencies. By inspecting Figure 3 and Figure 5 and having in mind the wavelet coefficient histogram, it is observed that small values of the wavelet coefficients are associated with large noise components in low spatial frequencies, while higher values of the wavelet coefficients can be associated to higher values of detector noise in higher spatial frequencies. Therefore the histogram of the Morlet wavelet coefficients can provide information regarding the spatial frequency distribution of detector noise. Images for this section: Page 6 of 9

7 Fig. 3: Figure 3: The NPS curves of the digital detector image (a) and the phosphor screen (b) Page 7 of 9

8 Fig. 4: Figure 4: Histogramm of the wavelet coefficients Fig. 5: Figure 5: Noise Transfer Function (NTF) of the digital detector and th phosphor screen Page 8 of 9

9 Conclusion Image noise images were evaluated with Fourier Transform and wavelet transform methods, using Morlet wavelet. It has been shown that, low values of the wavelet coefficient values, corresponds to increased noise in low spatial frequencies (i.e. due to in-homogeneities), while high values of the coefficient can be associated with increased higher spatial frequency noise. Personal information N. Kalyvas, S. Angelakis, A. Poulakis, S. Tsantis, C. Michail, G. Fountos, I Valais, I. Kandarakis are affiliated with the: Department of Biomedical Engineering, Technological Educational Institute of Athens, Ag. Spyridonos, 12210, Egaleo, Athens, Greece. correspondence nkalyvas@teiath.gr References J.T. Dobbins III, E. Samei, N.T. Ranger, Y. Chen "Intercomparison of methods for image quality. II Noise Power Spectrum", Med. Phys. 33(5), , J.F. Kirby "Which wavelet best reproduces the Fourier power spectrum?", Computers & Geosciences, 31, , Kalivas N., Valais I., Nikolopoulos D., Konstantinidis A.: et al.: "Light emission efficiency and imaging properties of YAP:Ce granular phosphor screens" Appl. Phys. A, 89, , 2007 Page 9 of 9