WavmatND: A MATLAB Package for Non-Decimated Wavelet Transform and its Applications

TL;DR

WavmatND is a MATLAB package that efficiently implements the non-decimated wavelet transform, supporting signals of arbitrary size and enabling easier inverse transforms, with applications in signal processing tasks.

Contribution

The paper introduces WavmatND, a MATLAB package with novel features for efficient NDWT computation, inverse transform facilitation, and support for non-dyadic signal sizes.

Findings

Reduces computation time for NDWT using matrix multiplications.

Enables straightforward inverse transforms via rescaled submatrices.

Supports non-dyadic and rectangular signals without size constraints.

Abstract

A non-decimated wavelet transform (NDWT) is a popular version of wavelet transforms because of its many advantages in applications. The inherent redundancy of this transform proved beneficial in tasks of signal denoising and scaling assessment. To facilitate the use of NDWT, we built a MATLAB package, {\bf WavmatND}, which has three novel features: First, for signals of moderate size the proposed method reduces computation time of the NDWT by replacing repetitive convolutions with matrix multiplications. Second, submatrices of an NDWT matrix can be rescaled, which enables a straightforward inverse transform. Finally, the method has no constraints on a size of the input signal in one or in two dimensions, so signals of non-dyadic length and rectangular two-dimensional signals with non-dyadic sides can be readily transformed. We provide illustrative examples and a tutorial to assist users in application of this stand-alone package.