Quantum Mechanics-Based Signal and Image Representation: Application to Denoising

Decomposition of digital signals and images into other basis or dictionaries than time space domains is a very common approach in signal image processing analysis. Such decomposition commonly obtained using fixed transforms (e.g., Fourier wavelet) learned from example databases the itself. In this work, we investigate detail new constructing such image-dependent bases inspired by quantum mechanics tools, i.e., considering as potential discretized Schroedinger equation. To illustrate proposed decomposition, denoising results are reported case Gaussian, Poisson, speckle noise compared to state art algorithms based on wavelet shrinkage, total variation regularization patch-wise sparse coding dictionaries, non-local means denoising, graph processing.