Related papers: Image representation and denoising using squared e…
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…
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…
Recently, a new Signal processing method, named Semi-Classical Signal Analysis (SCSA), has been proposed for denoising Magnetic Resonance Spectroscopy (MRS) signals. It is based on the Schr\"odinger Operator's eigenspectrum. It allows an…
In this study, we propose a novel image contrast enhancement method based on projecting images onto the squared eigenfunctions of the two-dimensional Schr\"odinger operator. This projection relies on a design parameter, $\gamma$, which…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
This article introduces a new signal analysis method. The main idea consists in interpreting a pulse-shaped signal, after multiplying it by a positive parameter, as a potential of a Schr\"odinger operator and representing this signal with…
Random operators may acquire extended states formed from a multitude of mutually resonating local quasi-modes. This mechanics is explored here in the context of the random Schr\"odinger operator on the complete graph. The operators exhibits…
This article addresses the image denoising problem in the situations of strong noise. We propose a dual sparse decomposition method. This method makes a sub-dictionary decomposition on the over-complete dictionary in the sparse…
This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called…
We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…
Exploiting a priori known structural information lies at the core of many image reconstruction methods that can be stated as inverse problems. The synthesis model, which assumes that images can be decomposed into a linear combination of…
We present a semi-sparsity model for 3D triangular mesh denoising, which is motivated by the success of semi-sparsity regularization in image processing applications. We demonstrate that such a regularization model can be also applied for…
With the inexorable digitalisation of the modern world, every subset in the field of technology goes through major advancements constantly. One such subset is digital images which are ever so popular. Images can not always be as visually…
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…
This article describes a fast iterative algorithm for image denoising and deconvolution with signal-dependent observation noise. We use an optimization strategy based on variable splitting that adapts traditional Gaussian noise-based…
In this paper, we propose an interpretable denoising method for graph signals using regularization by denoising (RED). RED is a technique developed for image restoration that uses an efficient (and sometimes black-box) denoiser in the…
During the acquisition of an image from its source, noise always becomes an integral part of it. Various algorithms have been used in past to denoise the images. Image denoising still has scope for improvement. Visual information…
We present a method for supervised learning of sparsity-promoting regularizers for image denoising. Sparsity-promoting regularization is a key ingredient in solving modern image reconstruction problems; however, the operators underlying…
Machine learning techniques work best when the data used for training resembles the data used for evaluation. This holds true for learned single-image denoising algorithms, which are applied to real raw camera sensor readings but, due to…
We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large distance. We show that this operator possesses a sequence of…