Related papers: Image representation and denoising using squared e…

In this article, we analyze the propagation of Wigner measures of a family of solutions to a system of semi-classical pseudodifferential equations presenting eigenvalues crossings on hypersurfaces. We prove the propagation along classical…

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…

The aim of this article is to analyze numerical schemes using two-layer neural networks withinfinite width for the resolution of high-dimensional Schr{\"o}dinger eigenvalue problems with smoothinteraction potentials and Neumann boundary…

Unpaired image denoising has achieved promising development over the last few years. Regardless of the performance, methods tend to heavily rely on underlying noise properties or any assumption which is not always practical. Alternatively,…

Optical full-field techniques have a great importance in modern experimental mechanics. Even if they are reasonably spread among the university laboratories, their diffusion in industrial companies remains very narrow for several reasons,…

In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local…

The bilateral filter is a useful nonlinear filter which without smoothing edges, it does spatial averaging. In the literature, the effectiveness of this method for image denoising is shown. In this paper, an extension of this method is…

The advancement of imaging devices and countless images generated everyday pose an increasingly high demand on image denoising, which still remains a challenging task in terms of both effectiveness and efficiency. To improve denoising…

Let (M,g) be a n-dimensional compact Riemannian manifold. We consider the magnetic deformations of semiclassical Schrodinger operators on M for a family of magnetic potentials that depends smoothly on $k$ parameters $u$, for $k \geq n$, and…

Deep learning methods have become the state of the art for undersampled MR reconstruction. Particularly for cases where it is infeasible or impossible for ground truth, fully sampled data to be acquired, self-supervised machine learning…

This paper concerns the numerical approximation of low-energy eigenstates of the linear random Schr\"odinger operator. Under oscillatory high-amplitude potentials with a sufficient degree of disorder it is known that these eigenstates…

Large amount of image denoising literature focuses on single channel images and often experimentally validates the proposed methods on tens of images at most. In this paper, we investigate the interaction between denoising and…

A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…

Self-supervised learning for image denoising problems in the presence of denaturation for noisy data is a crucial approach in machine learning. However, theoretical understanding of the performance of the approach that uses denatured data…

Image denoising is a well-known and well studied problem, commonly targeting a minimization of the mean squared error (MSE) between the outcome and the original image. Unfortunately, especially for severe noise levels, such Minimum MSE…

Modern signal and image acquisition systems are able to capture data that is no longer real-valued, but may take values on a manifold. However, whenever measurements are taken, no matter whether manifold-valued or not, there occur tiny…

We report on a particular example of noise and data representation interacting to introduce systematic error. Many instruments collect integer digitized values and appy nonlinear coding, in particular square-root coding, to compress the…

The rise of machine learning in image processing has created a gap between trainable data-driven and classical model-driven approaches: While learning-based models often show superior performance, classical ones are often more transparent.…

Wavelets are closely related to the Schr\"odinger's wave functions and the interpretation of Born. Similarly to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach…

We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…