Block-median pyramidal transform: analysis and denoising applications

A nonlinear multiscale pyramidal transform based on nonoverlapping block decompositions using the median operation and a polynomial approximation is considered. It is shown that this structure can be useful for denoising of oneand two-dimensional (1-D and 2-D) signals. Various denoising techniques are analyzed, including methods based on spatially adaptive thresholding and partial cycle-spinning algorithms. An analytical method for deriving the distribution function of the transform coefficients is also presented. This, in turn, can be used for the selection of thresholds for denoising applications.

[1]  Jaakko Astola,et al.  New algorithm for removing mixed (white and impulsive) noise from images , 1999, Electronic Imaging.

[2]  Ronald R. Coifman,et al.  In Wavelets and Statistics , 1995 .

[3]  Keshab K. Parhi,et al.  A wavelet-domain algorithm for denoising in the presence of noise outliers , 1997, Proceedings of International Conference on Image Processing.

[4]  George K. Matsopoulos,et al.  Data Cylinders in Medical Image Fusion , 1995 .

[5]  Ricardo L. de Queiroz,et al.  A pyramidal coder using a nonlinear filter bank , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[6]  Göran Salomonsson,et al.  Image enhancement based on a nonlinear multiscale method , 1997, IEEE Trans. Image Process..

[7]  Luciano Alparone,et al.  Multiresolution adaptive filtering of signal-dependent noise based on a generalized Laplacian pyramid , 1997, Proceedings of International Conference on Image Processing.

[8]  Reginald L. Lagendijk,et al.  Noise reduction for image sequences using an oriented pyramid thresholding technique , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[9]  King Ngi Ngan,et al.  A frequency scalable coding scheme employing pyramid and subband techniques , 1994, IEEE Trans. Circuits Syst. Video Technol..

[10]  A. Antoniadis,et al.  Wavelets and Statistics , 1995 .

[11]  Ioannis Pitas,et al.  Nonlinear Digital Filters - Principles and Applications , 1990, The Springer International Series in Engineering and Computer Science.

[12]  Richard G. Baraniuk,et al.  Statistical signal processing using wavelet-domain hidden Markov models , 1997, Optics & Photonics.

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

[14]  R. Oktem,et al.  Image compression using pyramidal distance order statistic filtering , 1996, 1996 IEEE Digital Signal Processing Workshop Proceedings.

[15]  O. Yli-Harja.  Formula for the joint distribution of stack filters , 1994, IEEE Signal Processing Letters.

[16]  Jaakko Astola,et al.  Iterative block-median pyramid transform-based denoising , 1999, Optics & Photonics.

[17]  Fionn Murtagh,et al.  Multiresolution and Astronomical Image Processing , 1995 .

[18]  Jean-Marc Boucher,et al.  Unsupervised multiscale speckle filtering , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[19]  Edward H. Adelson,et al.  The Laplacian Pyramid as a Compact Image Code , 1983, IEEE Trans. Commun..

[20]  Awad Kh. Al-Asmari.  Optimum bit rate pyramid coding with low computational and memory requirements , 1995, IEEE Trans. Circuits Syst. Video Technol..

[21]  Henk J. A. M. Heijmans,et al.  Some thoughts on morphological pyramids and wavelets , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[22]  Ronald W. Schafer,et al.  A non-expansive pyramidal morphological image coder , 1994, Proceedings of 1st International Conference on Image Processing.

[23]  Fionn Murtagh,et al.  Image Processing and Data Analysis - The Multiscale Approach , 1998 .

[24]  William A. Pearlman,et al.  A clustering algorithm for entropy-constrained vector quantizer design with applications in coding image pyramids , 1995, IEEE Trans. Circuits Syst. Video Technol..

[25]  Martin Vetterli,et al.  Spatially adaptive wavelet thresholding with context modeling for image denoising , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[26]  Granino A. Korn,et al.  Mathematical handbook for scientists and engineers. Definitions, theorems, and formulas for reference and review , 1968 .

[27]  Edward J. Coyle,et al.  Stack filters , 1986, IEEE Trans. Acoust. Speech Signal Process..

[28]  Fionn Murtagh,et al.  Astronomical Image Compression Using the Pyramidal Median Transform , 1995 .

[29]  Hervé Carfantan,et al.  Time-invariant orthonormal wavelet representations , 1996, IEEE Trans. Signal Process..

[30]  Tao Yu,et al.  Robust nonlinear wavelet transform based on median-interpolation , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[31]  Jaakko Astola,et al.  Image denoising using a block-median pyramid , 1999, Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348).