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We present an approach for variational regularization of inverse and imaging problems for recovering functions with values in a set of vectors. We introduce regularization functionals, which are derivative-free double integrals of such…

Optimization and Control · Mathematics 2018-12-24 René Ciak , Melanie Melching , Otmar Scherzer

In image processing, classical methods minimize a suitable functional that balances between computational feasibility (convexity of the functional is ideal) and suitable penalties reflecting the desired image decomposition. The fact that…

Computer Vision and Pattern Recognition · Computer Science 2020-10-20 Robin Richter , Duy H. Thai , Stephan F. Huckemann

Dimension reduction techniques are often used when the high-dimensional tensor has relatively low intrinsic rank compared to the ambient dimension of the tensor. The CANDECOMP/PARAFAC (CP) tensor completion is a widely used approach to find…

Numerical Analysis · Mathematics 2021-04-01 Jiahua Jiang , Fatoumata Sanogo , Carmeliza Navasca

Inverse problems in image processing are typically cast as optimization tasks, consisting of data-fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two…

Image and Video Processing · Electrical Eng. & Systems 2020-10-30 Regev Cohen , Michael Elad , Peyman Milanfar

Deep neural networks trained as image denoisers are widely used as priors for solving imaging inverse problems. While Gaussian denoising is thought sufficient for learning image priors, we show that priors from deep models pre-trained as…

Image and Video Processing · Electrical Eng. & Systems 2024-10-04 Yuyang Hu , Albert Peng , Weijie Gan , Peyman Milanfar , Mauricio Delbracio , Ulugbek S. Kamilov

We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These…

Optimization and Control · Mathematics 2014-12-12 Andreas Weinmann , Laurent Demaret , Martin Storath

We study the problem of deconvolution for light-sheet microscopy, where the data is corrupted by spatially varying blur and a combination of Poisson and Gaussian noise. The spatial variation of the point spread function (PSF) of a…

We consider multichannel deconvolution in a periodic setting with long-memory errors under three different scenarios for the convolution operators, i.e., super-smooth, regular-smooth and box-car convolutions. We investigate global…

Statistics Theory · Mathematics 2014-05-07 Rafal Kulik , Theofanis Sapatinas , Justin Rory Wishart

In this paper we extend the state-of-the-art filtered backprojection (FBP) method with application of the concept of Total Variation regularization. We compare the performance of the new algorithm with the most common form of regularizing…

In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…

Numerical Analysis · Mathematics 2022-09-14 Alireza Hosseini

Solving inverse problems \(Ax = y\) is central to a variety of practically important fields such as medical imaging, remote sensing, and non-destructive testing. The most successful and theoretically best-understood method is convex…

Numerical Analysis · Mathematics 2025-09-23 Daniel Obmann , Gyeongha Hwang , Markus Haltmeier

We study a general total variation denoising model with weighted $L^1$ fidelity, where the regularizing term is a non-local variation induced by a suitable (non-integrable) kernel $K$, and the approximation term is given by the $L^1$ norm…

Functional Analysis · Mathematics 2023-07-11 Konstantinos Bessas , Giorgio Stefani

We have shown that the vector of the point spread function (PSF) lexicographical presentation belongs to the left side conjugated null space (NS) of the autoregression (AR) matrix operator on condition the AR parameters are common for…

Computer Vision and Pattern Recognition · Computer Science 2015-03-02 Yuriy A. Bunyak , Roman N. Kvetnyy , Olga Yu. Sofina

This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…

Numerical Analysis · Mathematics 2009-05-15 Massimo Fornasier , Andreas Langer , Carola-Bibiane Schönlieb

This paper demonstrates a practical method that can correct spatial varying blur from a set of images of the same object. The algorithm jointly estimates the object and local point spread functions~(PSF). The method prioritizes sections…

Image and Video Processing · Electrical Eng. & Systems 2020-11-04 Wouter van de Ketterij , Oleg Soloviev , Michel Verhaegen

The recent statistical theory of neural networks focuses on nonparametric denoising problems that treat randomness as additive noise. Variability in image classification datasets does, however, not originate from additive noise but from…

Statistics Theory · Mathematics 2025-08-19 Juntong Chen , Sophie Langer , Johannes Schmidt-Hieber

It's well-known that inverse problems are ill-posed and to solve them meaningfully one has to employ regularization methods. Traditionally, popular regularization methods have been the penalized Variational approaches. In recent years, the…

Machine Learning · Computer Science 2022-02-17 Abinash Nayak

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…

Optimization and Control · Mathematics 2008-03-25 François-Xavier Dupé , Jalal Fadili , Jean Luc Starck

The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…

Numerical Analysis · Mathematics 2015-12-01 Martin Burger , Jan Modersitzki , Sebastian Suhr

We consider the problem of denoising a function observed after a convolution with a random filter independent of the noise and satisfying some mean smoothness condition depending on an ill posedness coefficient. We establish the minimax…

Statistics Theory · Mathematics 2007-06-13 Thomas Willer