Quantum mechanics-based signal and image representation: application to denoising

Abstract

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

arXiv comment17 pages, 18 figures; complements and expands arXiv:1802.02358

References in corpus (3)

• Restoration of Poissonian Images Using Alternating Direction Optimization
• Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain
• Adaptive transform via quantum signal processing: application to signal and image denoising

Cited by in corpus (7)

• A Novel Image Denoising Algorithm Using Concepts of Quantum Many-Body Theory
• Plug-and-Play Quantum Adaptive Denoiser for Deconvolving Poisson Noisy Images
• Image Denoising Inspired by Quantum Many-Body physics
• Quantum Algorithm for Signal Denoising
• Automatic Tuning of Denoising Algorithms Parameters Without Ground Truth
• Hybrid classical-quantum image processing via polar Walsh basis functions
• DisQu: Investigating the Impact of Disorder in Quantum Generative Models