Potential MSE of color image local filtering in component-wise and vector cases

In this paper, we investigate the derivation of Cramer-Rao lower bounds on component-wise and vector filtering performance. For two state-of-the-art local (DCT) and non-local (BM3D) filters in both component-wise and vector realizations, filtering output MSEs are compared with their respectively derived CRLBs. The comparative analysis shows good correspondence for images with different content and different noise levels.

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

[2]  H. Cramér.  Mathematical methods of statistics , 1947 .

[3]  H. Lilliefors.  On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown , 1967 .

[4]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[5]  D. Wolfe,et al.  Nonparametric Statistical Methods. , 1974 .

[6]  Rafael C. González,et al.  Local Determination of a Moving Contrast Edge , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Alex Pentland,et al.  Fractal-Based Description of Natural Scenes , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[9]  J. Astola,et al.  Fundamentals of Nonlinear Digital Filtering , 1997 .

[10]  Nina S. N. Lam,et al.  Fractal Characterization of Hyperspectral Imagery , 1999 .

[11]  N. Lam,et al.  Multi-Scale Fractal Analysis of Image Texture and Pattern , 1999 .

[12]  K. Plataniotis,et al.  Color Image Processing and Applications , 2000 .

[13]  R. A. Vaughan,et al.  Multifractal analysis and feature extraction in satellite imagery , 2002 .

[14]  J. L. Véhel,et al.  Stochastic fractal models for image processing , 2002, IEEE Signal Process. Mag..

[15]  David G. Luenberger,et al.  Linear and Nonlinear Programming: Second Edition , 2003 .

[16]  David Zhang,et al.  Integrated image and graphics technologies , 2004 .

[17]  Nikolay N. Ponomarenko,et al.  Three-State Locally Adaptive Texture Preserving Filter for Radar and Optical Image Processing , 2005, EURASIP J. Adv. Signal Process..

[18]  James R. Schott,et al.  Matrix Analysis for Statistics , 2005 .

[19]  Nikolay N. Ponomarenko,et al.  Image Filtering Based on Discrete Cosine Transform , 2007 .

[20]  Charles Kervrann,et al.  Local Adaptivity to Variable Smoothness for Exemplar-Based Image Regularization and Representation , 2008, International Journal of Computer Vision.

[21]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[22]  Karen O. Egiazarian,et al.  Color Image Denoising via Sparse 3D Collaborative Filtering with Grouping Constraint in Luminance-Chrominance Space , 2007, 2007 IEEE International Conference on Image Processing.

[23]  Nikolay N. Ponomarenko,et al.  3D DCT Based Filtering of Color and Multichannel Images , 2008 .

[24]  Nikolay N. Ponomarenko,et al.  Color image database for evaluation of image quality metrics , 2008, 2008 IEEE 10th Workshop on Multimedia Signal Processing.

[25]  Peyman Milanfar,et al.  Clustering-Based Denoising With Locally Learned Dictionaries , 2009, IEEE Transactions on Image Processing.

[26]  V. Lukin,et al.  Non-parametric detection scheme for isotropic image texture with normal increments , 2010, 2010 International Conference on Mathematical Methods in Electromagnetic Theory.

[27]  Michael Elad,et al.  Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing , 2010 .

[28]  Vishal M. Patel.  Sparse and Redundant Representations for Inverse Problems and Recognition , 2010 .

[29]  Peyman Milanfar,et al.  Is Denoising Dead? , 2010, IEEE Transactions on Image Processing.