Denoising using linear and nonlinear multiresolutions II: cell‐average framework and color images

Purpose – Multiresolution representations of data are classical tools in image processing applications. The purpose of this paper is to discuss a particular problem, obtaining good reconstructions of noise images.Design/methodology/approach – A nonlinear multiresolution scheme within Harten's framework corresponding to a nonlinear cell‐average technique is used for color image denoising.Findings – This paper finds it is possible, for example, to apply the theoretical framework to case studies in internationally operating companies delivering a mix of goods and services.Research limitations/implications – The present study provides a starting point for further research in the denoising problems using nonlinear techniques.Originality/value – Moreover, the proposed framework has proven to be useful in improving the classical linear multiresolution approaches.

[1]  P. W. Jones,et al.  Digital Image Compression Techniques , 1991 .

[2]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .

[3]  A. Harten,et al.  Multiresolution Based on Weighted Averages of the Hat Function I: Linear Reconstruction Techniques , 1998 .

[4]  Albert Cohen,et al.  Tensor product multiresolution analysis with error control for compact image representation , 2002, Signal Process..

[5]  Francesc Aràndiga,et al.  Nonlinear multiscale decompositions: The approach of A. Harten , 2000, Numerical Algorithms.

[6]  I. Daubechies,et al.  Biorthogonal bases of compactly supported wavelets , 1992 .

[7]  En-Bing Lin,et al.  Image compression and denoising via nonseparable wavelet approximation , 2003 .

[8]  A. Harten Multiresolution representation of data: a general framework , 1996 .

[9]  Jacques Liandrat,et al.  Analysis of a New Nonlinear Subdivision Scheme. Applications in Image Processing , 2006, Found. Comput. Math..

[10]  Francesc Aràndiga,et al.  Multiresolution Based on Weighted Averages of the Hat Function II: Nonlinear Reconstruction Techniques , 1998, SIAM J. Sci. Comput..

[11]  Gilles Deslauriers,et al.  Symmetric iterative interpolation processes , 1989 .

[12]  A. Harti Discrete multi-resolution analysis and generalized wavelets , 1993 .

[13]  I. Daubechies Orthonormal bases of compactly supported wavelets , 1988 .

[14]  S. Osher,et al.  Some results on uniformly high-order accurate essentially nonoscillatory schemes , 1986 .

[15]  Charles A. Micchelli,et al.  Interpolatory Subdivision Schemes and Wavelets , 1996 .

[16]  Sergio Amat,et al.  Data Compression with ENO Schemes: A Case Study☆☆☆ , 2001 .

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

[18]  Sergio Amat,et al.  Nonlinear Harten's multiresolution on the quincunx pyramid , 2006 .

[19]  Sergio Amat,et al.  Denoising using linear and nonlinear multiresolutions , 2005 .

[20]  C. Micchelli,et al.  Biorthogonal Wavelet Expansions , 1997 .