A Unifying Decomposition and Reconstruction Model for Discrete Signals

TL;DR

This paper introduces a unifying framework for discrete signal decomposition and reconstruction that generalizes existing wavelet filtering banks, allowing for flexible, well-posed solutions with high accuracy validated by theoretical and experimental results.

Contribution

It presents a novel, unified framework for designing discrete signal filtering banks that encompasses existing wavelet methods and enables customizable, well-posed decomposition and reconstruction.

Findings

Framework generalizes many existing wavelet filtering banks.

Flexible constraints improve practical decomposition and reconstruction.

Experimental results confirm high accuracy and effectiveness.

Abstract

Decomposing discrete signals such as images into components is vital in many applications, and this paper propose a framework to produce filtering banks to accomplish this task. The framework is an equation set which is ill-posed, and thus have many solutions. Each solution can form a filtering bank consisting of two decomposition filters, and two reconstruction filters. Especially, many existing discrete wavelet filtering banks are special cases of the framework, and thus the framework actually makes the different wavelet filtering banks unifiedly presented. Moreover, additional constraints can impose on the framework to make it well-posed, meaning that decomposition and reconstruction (D&R) can consider the practical requirements, not like existing discrete wavelet filtering banks whose coefficients are fixed. All the filtering banks produced by the framework can behave excellently, have many decomposition effect and precise reconstruction accuracy, and this has been theoretically proved and been confirmed by a large number experimental results.