Translation-invariant denoising using the minimum description length criterion

A translation-invariant denoising method based on the minimum description length (MDL) criterion and treestructured best-basis algorithms is presented. A collection of signal models is generated using an extended library of orthonormal wavelet-packet bases, and an additive cost function, approximately representing the MDL principle, is derived. We show that the minimum description length of the noisy observed data is achieved by utilizing the shift-invarient wavelet packet decomposition (SIWPD) and thresholding the resulting coe$cients. This approach is extendable to local trigonometric decompositions, and corresponding procedures to optimize either the library of bases or the "lter banks used at each node of the expansion-tree are described. The signal estimator is e$ciently combined with a modi"ed Wigner distribution, yielding robust time}frequency representations, characterized by high resolution and suppressed interference-terms. The proposed method is compared to alternative existing methods, and its superiority is demonstrated by synthetic and real data examples. ( 1999 Elsevier Science B.V. All rights reserved.