MDL-based translation-invariant denoising and robust time-frequency representations

Abstract

A translation-invariant denoising method, based on the minimum description length (MDL) criterion and the shift-invariant wavelet packet decomposition (SIWPD) 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 SIWPD and thresholding the resulting coefficients. The signal estimator is combined with a modified Wigner distribution, yielding robust time-frequency representations, characterized by the high resolution and suppressed interference-terms. The proposed method is compared with alternative approaches, and its superiority is demonstrated.