<title>Nonlinear processing of a shift-invariant discrete wavelet transform (DWT) for noise reduction</title>

Abstract

ABSTRACT A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in somewavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of theusual orthogonal one. Another difference is the shift invariance as opposed to the traditional orthogonal wavelettransform. We show that this new approach can be interpreted as a repeated application of Donoho's original method. The main feature is, however, a dramatically improved noise reduction compared to Donoho's approach,both in terms of the 12 error and visually, for a large class of signals. This is shown by theoretical and experimental results, including synthetic aperture radar (SAR) images.Keywords: noise reduction, shift invariance, redundancy, wavelet transform, SAR 1 INTRODUCTION Recently a novel approach for noise reduction due to Donoho and Johnstone'23 has been established. It employs thresholding in the wavelet domain and can be shown to be asymptotically near optimal for a wide class