Iterative methods for anisotropic diffusion of speckled medical images

This paper deals with filtering multiplicative noise that corrupts ultrasound medical images. The aim is to increase their contrast, while preserving edges and structures. From a mathematical point of view, this requires solving numerically an evolutive nonlinear boundary value problem. Several discretization schemes are studied for the stationary problem as well as for the evolutive problem. The behavior of various iterative methods is analyzed when semi-implicit time marching schemes are used. Results of sequential simulations are presented.

[1]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  R. Dautray,et al.  Analyse mathématique et calcul numérique pour les sciences et les techniques , 1984 .

[3]  P. Lions,et al.  Image selective smoothing and edge detection by nonlinear diffusion. II , 1992 .

[4]  O. Axelsson.  Iterative solution methods , 1995 .

[5]  Jean Claude Miellou,et al.  Optimization of the Relaxation Parameter for S.S.O.R. and A.D.I. Preconditioning , 2004, Numerical Algorithms.

[6]  Jacques M. Bahi,et al.  Evaluations of Parameters for the Optimization of S.S.O.R. and A.D.I. Preconditioning , 2004, Numerical Algorithms.

[7]  M. Braga,et al.  Exploratory Data Analysis , 2018, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[8]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[9]  Guillermo Sapiro,et al.  Robust anisotropic diffusion , 1998, IEEE Trans. Image Process..

[10]  Max A. Viergever,et al.  Efficient and reliable schemes for nonlinear diffusion filtering , 1998, IEEE Trans. Image Process..

[11]  J. Craggs.  Applied Mathematical Sciences , 1973 .

[12]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[13]  Pierre Kornprobst,et al.  Mathematical problems in image processing - partial differential equations and the calculus of variations , 2010, Applied mathematical sciences.

[14]  Hadj Batatia,et al.  A robust speckle reducing anisotropic diffusion , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[15]  M. Barlaud,et al.  Nonlinear image processing: modeling and fast algorithm for regularization with edge detection , 1995, Proceedings., International Conference on Image Processing.

[16]  Joachim Weickert,et al.  Anisotropic diffusion in image processing , 1996 .

[17]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[18]  Scott T. Acton,et al.  Speckle reducing anisotropic diffusion , 2002, IEEE Trans. Image Process..