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We present a novel variational approach to image restoration (e.g., denoising, inpainting, labeling) that enables to complement established variational approaches with a histogram-based prior enforcing closeness of the solution to some…

Optimization and Control · Mathematics 2013-07-18 Paul Swoboda , Christoph Schnörr

Numerous total variation (TV) regularizers, engaged in image restoration problem, encode the gradients by means of simple $[-1,1]$ FIR filter. Despite its low computational processing, this filter severely deviates signal's high frequency…

Optimization and Control · Mathematics 2015-06-17 Mahdi S. Hosseini , Konstantinos N. Plataniotis

We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…

Information Theory · Computer Science 2015-10-28 Sohail Bahmani , Justin Romberg

This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm…

Machine Learning · Computer Science 2018-08-20 Fahad Shamshad , Ali Ahmed

We introduce a compressive single-pixel imaging (SPI) framework for high-resolution image capture in fractions of a second. This framework combines a dedicated sampling strategy with a tailored reconstruction method to enable high-quality…

Image and Video Processing · Electrical Eng. & Systems 2025-09-03 Anna Pastuszczak , Rafał Stojek , Piotr Wróbel , Magdalena Cwojdzińska , Kacper Sobczak , Rafał Kotyński

In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…

Numerical Analysis · Mathematics 2022-11-15 Valerio Pagliari , Kostas Papafitsoros , Bogdan Raiţă , Andreas Vikelis

In this paper, we investigate the application of continuous sparse signal reconstruction algorithms for the estimation of the ranges and speeds of multiple moving targets using an FMCW radar. Conventionally, to be reconstructed, continuous…

Signal Processing · Electrical Eng. & Systems 2021-02-11 Gilles Monnoyer de Galland , Thomas Feuillen , Luc Vandendorpe , Laurent Jacques

We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common…

Machine Learning · Statistics 2015-06-03 Sampurna Biswas , Sunrita Poddar , Soura Dasgupta , Raghuraman Mudumbai , Mathews Jacob

It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing explicit constraints on the recovered matrix, such as the…

Machine Learning · Computer Science 2022-06-28 Zhemin Li , Zhi-Qin John Xu , Tao Luo , Hongxia Wang

In the Fourier frequency domain, luminance information is primarily encoded in the amplitude component, while spatial structure information is significantly contained within the phase component. Existing low-light image enhancement…

Computer Vision and Pattern Recognition · Computer Science 2024-12-03 Tongshun Zhang , Pingping Liu , Ming Zhao , Haotian Lv

As vision based perception methods are usually built on the normal light assumption, there will be a serious safety issue when deploying them into low light environments. Recently, deep learning based methods have been proposed to enhance…

Computer Vision and Pattern Recognition · Computer Science 2020-10-21 Junjie Hu , Xiyue Guo , Junfeng Chen , Guanqi Liang , Fuqin Deng , Tin lun Lam

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…

Machine Learning · Statistics 2019-09-12 Tomas Vaškevičius , Varun Kanade , Patrick Rebeschini

Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…

Numerical Analysis · Mathematics 2024-06-26 Andrea Ebner , Matthias Schwab , Markus Haltmeier

This paper addresses the problem of inverse rendering from photometric images. Existing approaches for this problem suffer from the effects of self-shadows, inter-reflections, and lack of constraints on the surface reflectance, leading to…

Computer Vision and Pattern Recognition · Computer Science 2025-04-09 Jingzhi Bao , Guanying Chen , Shuguang Cui

Ultra-high-definition (UHD) image restoration poses unique challenges due to the high spatial resolution, diverse content, and fine-grained structures present in UHD images. To address these issues, we introduce a progressive spectral…

Computer Vision and Pattern Recognition · Computer Science 2026-04-20 Chen Zhao , Yunzhe Xu , Zhizhou Chen , Enxuan Gu , Kai Zhang , Xiaoming Liu , Jian Yang , Ying Tai

Despite significant advancements in automatic brain tumor segmentation methods, their performance is not guaranteed when certain MR sequences are missing. Addressing this issue, it is crucial to synthesize the missing MR images that reflect…

Image and Video Processing · Electrical Eng. & Systems 2024-12-03 Jihoon Cho , Seunghyuck Park , Jinah Park

Image restoration refers to the process of reconstructing noisy, destroyed, or missing parts of an image, which is an ill-posed inverse problem. A specific regularization term and image degradation are typically assumed to achieve…

Image and Video Processing · Electrical Eng. & Systems 2025-04-15 Jianwei Ke

This work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systems pose a challenge for iterative image…

Medical Physics · Physics 2016-11-17 Emil Y. Sidky , Rick Chartrand , Yuval Duchin , Christer Ullberg , Xiaochuan Pan

Conventional sensor architectures typically restrict angle estimation to the half-space. By enabling simultaneous transmission and reflection, simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) can…

Signal Processing · Electrical Eng. & Systems 2026-02-04 Ziming Liu , Tao Chen , Muran Guo , Francesco Verde

Matrix completion is about recovering a matrix from its partial revealed entries, and it can often be achieved by exploiting the inherent simplicity or low dimensional structure of the target matrix. For instance, a typical notion of matrix…

Information Theory · Computer Science 2019-10-08 Jinchi Chen , Weiguo Gao , Ke Wei
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