Abstract
In this paper, we consider two variational models for speckle reduction of ultrasound images. By employing the G-convergence argument we show that the solution of the SO model coincides with the minimizer of the JY model. Furthermore, we incorporate the split Bregman technique to propose a fast alterative algorithm to solve the JY model. Some numerical experiments are presented to illustrate the efficiency of the proposed algorithm.
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Aubert, G., Aujol, J.F. A variational approach to removing multiplicative noise. SIAM J. Appl. Math., 68: 925–946 (2008)
Bioucas-Dias, J.M. Figueiredo. Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization. IEEE Transactions on Image Processing, 19(7): 1720–1730, (2010)
Darbon, J., Sigelle, M., Tupin, F. A Note on Nice-Levelable MRFs for SAR Image Denoising with Contrast Preservation. Technical Report, 2006
Dutt, V., Greenleaf, J. Statistics of the Log-Compression Envelope. Journal of Acoustical Society of America, 99(6): 3817–3825 (1996)
Ekeland, I., Témam, R. Convex Analysis and Variational Problems. SIAM, Philadelphia, 1999
Maso, G.D. An introduction to G-convergence. Birkhäuser, Boston, 1993
Evans, L.C. Partial differential equations. American Mathematical Society, 1998
Evans, L.C., Gariepy, R.F. Measure Thoery and Fine Properties of Functions. CRC Press, 1992
Giusti, F. Minimal Surfaces and Functions of Bounded Variation, Monographs in Math., Vol. 80, Brikhäuser, Basel, 1984
Goldstein, T., Osher, S. The split Bregman method for L1 regularized problems. SIAM Journal on Imaging Sciences, 2(2): 323–343 (2009)
Huang, Y., Ng, M., Wen, Y. A new total variation method for multiplicative noise removal. SIAM Journal on Imaging Science, 2(1): 20–40 (2009)
Jin, Z.M., Yang, X.P. A Variational Model to Remove the Multiplicative Noise in Ultrasound Images. Journal of Mathematical Imaging and Vision, 39: 62–74 (2011)
Kaplan, D., Ma, Q. On the statistical characteristics of the log-compressed rayleigh signals: Theorical formulation and experimental results. J. Acoust. Soc. Amer., 95: 1396–1400 (1994)
Lin, F.H., Yang, X.P. Geometric measure theory-an introduction. Science Press and International Press, Beijing, Boston, 2002
Loupas, A. Digital image processing for noise reduction in medical ultrasonics. PhD Thesis, University of Edinburgh, UK, 1988
Rudin, L., Lions, P.L., Osher, S. Multiplicative denoising and deblurring: Theory and algorithms. In: S. Osher and N. Paragios, editors, Geometric Level Sets in Imaging, Vision, and Graphics, Springer-Verlag, 2003, 103–119
Rudin, L., Osher, S., Fatemi, E. Nonlinear total variation based noise removal algorithms. Physica D, 60: 259–268 (1992)
Shi, J., Osher, S. A nonlinear inverse scale space method for a convex multiplicative noise model. SIAM J. Imaging Sciences, 1: 294–321 (2008)
Steidl, G., Teuber, T. Removing multiplicative noise by Douglas-Rachford splitting methods. Journal of Mathematical Imaging and Vision, 36: 168–184 (2010)
Thijssen, J.M., Oosterveld, B.J., Wanger, R.F. Gray level transforms and lesion detectabivity in echographic images. Utrason. Imag., 10: 171–195 (1988)
Tuthill, T.A., Sperry, R.H., Parker, K.J. Deviation from Rayleigh statistics in ultrasonic spekle. Ultrason. Imag., 10: 81–90 (1988)
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Supported by the National Natural Science Foundation of China under Grants No. 11671004 and 91330101, and Natural Science Foundation for Colleges and Universities in Jiangsu Province under Grants No. 15KJB110018 and 14KJB110020.
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Jin, Zm., Yang, Xp. An analysis of two variational models for speckle reduction of ultrasound images. Acta Math. Appl. Sin. Engl. Ser. 32, 969–982 (2016). https://doi.org/10.1007/s10255-016-0618-1
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DOI: https://doi.org/10.1007/s10255-016-0618-1