Adaptive transform via quantum signal processing: application to signal and image denoising

TL;DR

This paper introduces an innovative adaptive transform based on quantum mechanics principles, specifically the Schrödinger equation, for signal and image denoising, demonstrating its effectiveness on signal-dependent noise.

Contribution

It presents a novel quantum-inspired transform constructed from the Schrödinger equation for improved signal and image denoising applications.

Findings

Effective denoising of signal-dependent noise

Demonstrates practical application of quantum-inspired transforms

Outperforms traditional methods in specific noise scenarios

Abstract

The main scope of this paper is to show how tools from quantum mechanics, in particular the Schroedinger equation, can be used to construct an adaptive transform suitable for signal and image processing applications. The proposed dictionary is obtained by considering the signal or image as a discrete potential in Schroedinger equation, further used to construct the Hamiltonien operator. In order to illustrate its practical interest in signal and image processing, we provide denoising results in the case of signal-dependent noise, which is the noise type the most adapted to the proposed approach.