Journal
IEEE OPEN JOURNAL OF SIGNAL PROCESSING
Volume 2, Issue -, Pages 190-206Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/OJSP.2021.3067507
Keywords
Quantum mechanics; Noise reduction; Oscillators; Transforms; Signal processing; Wave functions; Dictionaries; Adaptive signal and image representation; adaptive transformation; denoising; quantum mechanics
Categories
Funding
- CNRS
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The study investigates a new approach for constructing signal or image-dependent bases inspired by quantum mechanics tools, considering them as potentials in the discretized Schroedinger equation. Experimental results demonstrate the potential of this decomposition method for denoising under Gaussian, Poisson, and speckle noise compared to other state of the art algorithms.
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.
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