Image denoising using scale-adaptive lifting schemes

The paper addresses the problem of image denoising using adaptive wavelet transforms. Two scale-adaptive versions of the wavelet transform are implemented and experimentally tested: the classical and the lifting one. In both of them exemplary test images are contaminated with noise, decomposed into several multiresolution levels, modified via soft thresholding (only detail subimages) and inversely synthesized. On each level the LL image from the previous stage is decomposed into LL, LH, HL and HIT subimages using different wavelet or predict/update lifting filters (L-lowpass, H-highpass). At each level as the best filters are chosen such ones, for which the normalized energy of the detail HH subimage is the lowest. Image denoising is realized by soft thresholding of all detail HH subimages only. Several test images are processed in the paper. Explicit equations for the design of lifting filters are presented.

[1]  Tomasz P. Zielinski,et al.  Filter design for adaptive lifting schemes , 2000, 2000 10th European Signal Processing Conference.

[2]  Robert D. Nowak,et al.  Adaptive wavelet transforms via lifting , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

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

[4]  R. L. Claypoole,et al.  Nonlinear wavelet transforms for image coding , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[5]  W. Sweldens.  The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[6]  Richard Baraniuk,et al.  Lifting construction of non-linear wavelet transforms , 1998, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Cat. No.98TH8380).