Total Variation-Based Image Noise Reduction With Generalized Fidelity Function

In this letter, we analyze the relationship between the change in the intensity value and the scale of an image feature, when a generalized function is used as the fidelity term in the total variation-based noise removal scheme. Based on the analysis, we propose a designing method of the fidelity function that results in any desired monotonic relationship between the intensity change and the scale. As an example, we designed a fidelity function that results in a larger contrast between the intensity change of a small scaled feature and that of a large scaled one than the original total variation-based noise removal scheme that uses the norm as the fidelity function.

[1]  G. Aubert,et al.  Modeling Very Oscillating Signals. Application to Image Processing , 2005 .

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

[3]  Tony F. Chan,et al.  Scale Recognition, Regularization Parameter Selection, and Meyer's G Norm in Total Variation Regularization , 2006, Multiscale Model. Simul..

[4]  Jesús Ildefonso Díaz Díaz,et al.  Some qualitative properties for the total variation flow , 2002 .

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

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

[7]  Donald Geman,et al.  A nonlinear filter for film restoration and other problems in image processing , 1992, CVGIP Graph. Model. Image Process..

[8]  T. Chan,et al.  Edge-preserving and scale-dependent properties of total variation regularization , 2003 .

[9]  Donald Geman,et al.  Nonlinear image recovery with half-quadratic regularization , 1995, IEEE Trans. Image Process..

[10]  Tony F. Chan,et al.  Aspects of Total Variation Regularized L[sup 1] Function Approximation , 2005, SIAM J. Appl. Math..

[11]  Mila Nikolova,et al.  Regularizing Flows for Constrained Matrix-Valued Images , 2004, Journal of Mathematical Imaging and Vision.

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

[13]  M. Novaga,et al.  The Total Variation Flow in RN , 2002 .

[14]  Antonin Chambolle,et al.  Image Decomposition into a Bounded Variation Component and an Oscillating Component , 2005, Journal of Mathematical Imaging and Vision.

[15]  Mila Nikolova,et al.  Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers , 2002, SIAM J. Numer. Anal..

[16]  N. Sochen,et al.  Texture Preserving Variational Denoising Using an Adaptive Fidelity Term , 2003 .

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

[18]  Tony F. Chan,et al.  Structure-Texture Image Decomposition—Modeling, Algorithms, and Parameter Selection , 2006, International Journal of Computer Vision.

[19]  Donald Geman,et al.  Constrained Restoration and the Recovery of Discontinuities , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Stanley Osher,et al.  Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing , 2003, J. Sci. Comput..

[21]  Suk-Ho Lee,et al.  Noise removal with Gauss curvature-driven diffusion , 2005, IEEE Transactions on Image Processing.

[22]  Wotao Yin,et al.  Image Cartoon-Texture Decomposition and Feature Selection Using the Total Variation Regularized L1 Functional , 2005, VLSM.