III WVC 2007 - Iris.sel.eesc.sc.usp.br - USP

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WVC'2007 - III Workshop de Visão Computacional, 22 a 24 de Outubro de 2007, São José do Rio Preto, SP.(a)(b)(a) Original phantom (b) Wiener Filter (K =5)(c)Figure 3. Digital phantom in 3D (a) Breastphantom in (b) and VA image of the breastphantom (c)was convolved with the PSF (80 × 80 × 512) (Figure 4(a))and then Gaussian noise (µ =0, σ =0.5) was added to theblurred image. Figure 4(b) is the degraded image submittedto the restoration filters. Since the degraded image is complex,the figure shows the magnitude of an image slice: thex − y focal plane.(c) RLS Filter (γ =5) (d) GM Filter (γ = 1,K =5and α =1/2)Figure 5. Experimental resultsThe Wiener Filter and the RLS Filter algorithms producedgood results and also better results than the GeometricMean Filter. A visual inspection suggests that the RegularizedLeast Squares Filter is the best of them. To provethis observation, we used a quantitative measure to comparethe results: the Improvement in Signal to Noise Ratio(ISNR) [2]:()‖im d − im o ‖ 2ISNR =10∗ log 10‖im r − im o ‖ 2 . (14)where im d is the degraded image, im r is the restored imageand im o is the original image. According to this ratio, thehigher the value the better the restoration result. The resultsare resumed in Table 1.(a)Figure 4. Blurred image (a) and degradedimage (b)(b)Algorithm ISNRRLS 43.30Wiener 39.76Geometric Mean 31.17Table 1. ISNR of the resultsFigure 5(a) presents the original discrete phantom. Figures5(b), 5(c) and 5(d) present the results obtained afterrestoration using the Wiener Filter, the Regularized LeastSquares Filter (RLS) and the Geometric Mean Filter, respectively.One can notice that the restored images, as wellas the degraded image, exhibit characteristics of the PSF:artifacts in the same shape of the PSF lobules. The restorationresults are 3D matrices of real values just like the originaldiscrete phantom. After the restoration, the results maycontain imaginary parts, but those values are very small andhave no significance for the final result.As previously said, the results of the Geometric MeanFilter are close to those resulting from the Wiener or the InverseFilter. This could be the reason why this filter did notyielded a very good result. The result seems like the InverseFilter, that increases the noise impact on the image.Another approach that can be used to analyze the resultsis to apply a border detector to them. This technique is usefulbecause in this case the correct borders are known, i.e.,the ideal result has the same circular borders as the originalimage (phantom). The result of applying a Laplacian edgedetector (ED) to the restoration results is shown in Figure 6,39
WVC'2007 - III Workshop de Visão Computacional, 22 a 24 de Outubro de 2007, São José do Rio Preto, SP.where one sees that the RLS filtered image yielded the bestborders. As the result of the Geometric Mean was not sogood, the Laplacian detector was unable to find the borders.As previously discussed, the computational implementationposes problems when applying restoration algorithmsto vibro-acoustography images because of the characteristicsof the system. Thus, the computational cost of the implementationsshould also be compared. In this case, themethods used impose comparable computational costs.(a)Figure 6. ED for the Wiener Filter (a) and EDfor RLS Filter (b)7. ConclusionsWe presented an original and challenging problem:the application of restoration techniques to vibroacoustographyimages. The difficulties arising in thisapplication are discussed and solutions are presented, asthe overlap-add method used to overcome the memory requirementsimposed by size of the considered problem.This technique was successfully applied to our experimentaltests. We show results of three classical restorationtechniques applied to a new imaging modality, namely,the vibro-acoustography. There are various restoration methodsin the literature and this paper, indeed, is the first stepin this direction.We thank CNPq for Talita Perciano’s grant and Fapespfor the Thematic Project 2002/07153-2.References[1] H. C. Andrews and B. R. Hunt. Digital Image Restoration.Prentice-Hall, 1977.[2] A. C. Bovik. Handbook of Image and Video Processing.Academic Press, 2000.[3] E. O. Brigham. The Fast Fourier Transform. Prentice-Hall,Englewwod Cliffs, 1974.[4] I. Cespedes, J. Ophir, H. Ponnekanti, and N. Maklad. Elastography:elasticity imaging using ultrasound with applicationto muscle and breast in vivo. Ultrason Imaging, 15:73–88, 1993.(b)[5] M. Fatemi and J. F. Greenleaf. Ultrasound-Stimulated Vibro-Acoustic Spectrography. Science, 280:82–85, 1998.[6] M. Fatemi and J. F. Greenleaf. Vibro-acoustography: animaginf modality based on ultrasound-stimulated acousticemission. Proc. Natl. Acad. Sci. USA, 96:6603–6608, 1999.[7] L. Gao, K. J. Parker, R. M. Lerner, and S. F. Levinson. Imagingof the Elastic Properties of Tissue - A Review. Ult. Med.Biol., 22:959–977, 1996.[8] R. C. Gonzalez and R. E. Woods. Digital Image Processing.Addison-Wesley, MA, 1992.[9] J. F. Greenleaf, M. Fatemi, and M. Insana. Selected methodsfor imaging elastic properties of biological tissues. Annu RevBiomed Eng, 5:57–78, 2003.[10] A. K. Katsaggelos. Digital Image Restoration. Springer,New York, 1991.[11] E. Konofagou, J. D’hooge, and J. Ophir. Cardiac elastography- a feasible study. IEEE Ultrasonics Symposium Proceedings,2:1273–1276, 2000.[12] J. S. Lim. Two-Dimensional Signal and Image Processing.Prentice Hall, 1989.[13] R. Muthupillai, D. J. Lomas, P. J. Rossman, J. F. Greenleaf,A. Manduca, and R. L. Ehman. Magnetic resonance elastographyby direct visualization of propagating acoustic strainwaves. Science, 269:1854–1857, 1995.[14] K. Nightingale, M. S. Soo, R. Nightingale, and G. Trahey.Acoustic Radiation Force Impulse Imaging: In Vivo Demonstrationof Clinical Feasibility. Ultrasound in Medicine andBiology, 28:227–235, 2002.[15] J. Ophir, S. K. Alam, B. Garra, F. Kallel, E. Konofagou,T. Krouskop, and T. Varghese. Elastography: ultrasonic estimationand imaging of the elastic properties of tissues. Proc.Instn. Mech. Engrs., 213:203–233, 1999.[16] J. Ophir, I. Cespedes, H. Ponnekanti, Y. Yazdi, and X. Li.Elastography: a quantitative method for imaging the elasticityof biological tissues. Ultrason Imaging, 13:111–134,1991.[17] A. Sarvazyan. Handbook of Elastic Properties of Solids, Liquids,and Gases, volume Elastic Properties of Solids: Biologicaland Organic Materials, Earth and Marine Sciences,chapter 5. Academic Press, U.S., 2001.[18] A. P. Sarvazyan, O. V. Rudenko, S. D. Swanson, J. B.Fowlkes, and S. Y. Emelianov. Shear wave elasticity imaging:a new ultrasonic technology of medical diagnostics. Ultrasoundin Medicine and Biology, 24:1419–1435, 1998.[19] G. T. Silva, A. C. Frery, and M. Fatemi. Image Formation inVibro-acoustography with Depth-of-fields Effects. ComputerizedMedical Imaging and Graphics, 30:321–327, 2006.[20] T. Sugirnoto, S. Ueha, and K. Itoh. Tissue hardness measurementusing the radiation force of focused ultrasound.IEEE Ultrasonics Symposium Proceedings, pages 1377–1380, 1990.[21] W. F. Walker, F. J. Fernandez, and L. A. Negron. A methodof imaging viscoelastic parameters with acoustic radiationforce. Physics in Medicine and Biology, 45:1437–1447,2000.40
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