Total Variation Wavelet-Based Medical Image Denoising

We propose a denoising algorithm for medical images based on a combination of the total variation minimization scheme and the wavelet scheme. We show that our scheme offers effective noise removal in real noisy medical images while maintaining sharpness of objects. More importantly, this scheme allows us to implement an effective automatic stopping time criterion.

[1]  F. Malgouyres,et al.  Mathematical analysis of a model which combines total variation and wavelet for image restoration 1 , 2002 .

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

[3]  E. Candès,et al.  Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges , 2000 .

[4]  C. Vogel,et al.  Analysis of bounded variation penalty methods for ill-posed problems , 1994 .

[5]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[6]  Ge Wang,et al.  Evolution-Operator-Based Single-Step Method for Image Processing , 2006, Int. J. Biomed. Imaging.

[7]  R. Chan,et al.  Tight frame: an efficient way for high-resolution image reconstruction , 2004 .

[8]  Pavel Mrázek,et al.  Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering , 2001, International Journal of Computer Vision.

[9]  Yves Meyer,et al.  Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures , 2001 .

[10]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[11]  Jacques Froment,et al.  Artifact free signal denoising with wavelets , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[12]  S. Osher,et al.  IMAGE DECOMPOSITION AND RESTORATION USING TOTAL VARIATION MINIMIZATION AND THE H−1 NORM∗ , 2002 .

[13]  Yao Lu,et al.  Shadow block iteration for solving linear systems obtained from wavelet transforms , 2005 .

[14]  Stanley Osher,et al.  Image Decomposition and Restoration Using Total Variation Minimization and the H1 , 2003, Multiscale Model. Simul..

[15]  Jean-Michel Morel,et al.  A non-local algorithm for image denoising , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[16]  Martin J. Wainwright,et al.  Image denoising using scale mixtures of Gaussians in the wavelet domain , 2003, IEEE Trans. Image Process..

[17]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[18]  Antonin Chambolle,et al.  Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage , 1998, IEEE Trans. Image Process..

[19]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .

[20]  D. Dobson,et al.  Convergence of an Iterative Method for Total Variation Denoising , 1997 .

[21]  Josef Stoer,et al.  Numerische Mathematik 1 , 1989 .

[22]  Tony F. Chan,et al.  Euler's Elastica and Curvature-Based Inpainting , 2003, SIAM J. Appl. Math..

[23]  Tony F. Chan,et al.  Total Variation Wavelet Thresholding , 2007, J. Sci. Comput..

[24]  P. Lions,et al.  Image recovery via total variation minimization and related problems , 1997 .

[25]  Yehoshua Y. Zeevi,et al.  Estimation of optimal PDE-based denoising in the SNR sense , 2006, IEEE Transactions on Image Processing.

[26]  Joachim Weickert,et al.  Coherence-enhancing diffusion of colour images , 1999, Image Vis. Comput..

[27]  Tony F. Chan,et al.  The digital TV filter and nonlinear denoising , 2001, IEEE Trans. Image Process..

[28]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .