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Remote sensing image restoration aims to reconstruct missing or corrupted areas within images. To date, low-rank based models have garnered significant interest in this field. This paper proposes a novel low-rank regularization term, named…

Image and Video Processing · Electrical Eng. & Systems 2024-12-17 Shuang Xu , Chang Yu , Jiangjun Peng , Xiangyong Cao , Deyu Meng

During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to utilize sparsity assumptions to design powerful recovery algorithms of vectors…

Functional Analysis · Mathematics 2016-07-07 Axel Flinth

Weighted nuclear norm minimization has been recently recognized as a technique for reconstruction of a low-rank matrix from compressively sampled measurements when some prior information about the column and row subspaces of the matrix is…

Information Theory · Computer Science 2022-04-27 Hamideh Sadat Fazael Ardakani , Sajad Daei , Farzan Haddadi

The low-rank matrix recovery (LMR) is a rank minimization problem subject to linear equality constraints, and it arises in many fields such as signal and image processing, statistics, computer vision, system identification and control. This…

Information Theory · Computer Science 2011-06-17 Lingchen Kong , Levent Tunçel , Naihua Xiu

The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…

Information Theory · Computer Science 2018-05-31 Ali Bereyhi , Saeid Haghighatshoar , Ralf R. Müller

Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…

Information Theory · Computer Science 2017-01-31 Maxime Ferreira Da Costa , Wei Dai

We study the recovery of low-rank Hermitian matrices from rank-one measurements obtained by uniform sampling from complex projective 3-designs, using nuclear-norm minimization. This framework includes phase retrieval as a special case via…

Information Theory · Computer Science 2025-12-15 Timm Gilles

Consider the problem of reconstructing a multidimensional signal from an underdetermined set of measurements, as in the setting of compressed sensing. Without any additional assumptions, this problem is ill-posed. However, for signals such…

Numerical Analysis · Mathematics 2015-06-11 Deanna Needell , Rachel Ward

In this paper, we theoretically investigate the low-rank matrix recovery problem in the context of the unconstrained regularized nuclear norm minimization (RNNM) framework. Our theoretical findings show that, the RNNM method is able to…

Numerical Analysis · Mathematics 2021-03-09 Wendong Wang , Feng Zhang , Jianjun Wang

The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…

Information Theory · Computer Science 2014-07-21 Volker Pohl , Fanny Yang , Holger Boche

Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…

Numerical Analysis · Mathematics 2019-03-06 Chong-Jun Li , Yi-Jun Zhong

Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…

Information Theory · Computer Science 2023-08-08 Martin Genzel , Alexander Stollenwerk

We consider the problem of recovering the superposition of $R$ distinct complex exponential functions from compressed non-uniform time-domain samples. Total Variation (TV) minimization or atomic norm minimization was proposed in the…

Information Theory · Computer Science 2017-11-07 Weiyu Xu , Jirong Yi , Soura Dasgupta , Jian-Feng Cai , Mathews Jacob , Myung Cho

Super-resolution is generally referred to as the task of recovering fine details from coarse information. Motivated by applications such as single-molecule imaging, radar imaging, etc., we consider parameter estimation of complex…

Information Theory · Computer Science 2016-08-10 Dehui Yang , Gongguo Tang , Michael B. Wakin

We consider composite linear inverse problems where the signal to recover is modeled as a sum of two functions. We study a variational framework formulated as an optimization problem over the pairs of components using two regularization…

Optimization and Control · Mathematics 2026-05-25 Adrian Jarret , Julien Fageot

Let $T:H_1\rightarrow H_2$ be a bounded linear operator defined between complex Hilbert spaces $H_1$ and $H_2$. We say $T$ to be \textit{minimum attaining} if there exists a unit vector $x\in H_1$ such that $\|Tx\|=m(T)$, where…

Functional Analysis · Mathematics 2018-05-18 Neeru Bala , G. Ramesh

In this paper, we study the phase retrieval problem in the situation where the vector to be recovered has an a priori structure that can encoded into a regularization term. This regularizer is intended to promote solutions conforming to…

Optimization and Control · Mathematics 2024-07-24 Jean-Jacques Godeme , Jalal Fadili

We present improved sampling complexity bounds for stable and robust sparse recovery in compressed sensing. Our unified analysis based on l1 minimization encompasses the case where (i) the measurements are block-structured samples in order…

Information Theory · Computer Science 2020-05-22 Ben Adcock , Claire Boyer , Simone Brugiapaglia

In this note we study the problem of sampling and reconstructing signals which are assumed to lie on or close to one of several subspaces of a Hilbert space. Importantly, we here consider a very general setting in which we allow infinitely…

Information Theory · Computer Science 2009-12-02 Thomas Blumensath

We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…

Numerical Analysis · Mathematics 2026-01-21 Moritz Moeller , Sebastian Neumayer , Kateryna Pozharska , Tizian Sommerfeld , Tino Ullrich