相关论文: Super-resolved Lasso

In large-scale spatial surveys, such as the forthcoming ESA Euclid mission, images may be undersampled due to the optical sensors sizes. Therefore, one may consider using a super-resolution (SR) method to recover aliased frequencies, prior…

Waves from a sparse set of source hidden in additive noise are observed by a sensor array. We treat the estimation of the sparse set of sources as a generalized complex-valued LASSO problem. The corresponding dual problem is formulated and…

We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To recover the point sources, we propose to solve a convex…

The problem of finding the sparsest solution to a linear underdetermined system of equations, often appearing, e.g., in data analysis, optimal control, system identification, or sensor selection problems, is considered. This non-convex…

Compressed sensing (CS) schemes are proposed for monostatic as well as synthetic aperture radar (SAR) imaging with chirped signals and Ultra-Narrowband (UNB) continuous waveforms. In particular, a simple, perturbation method is developed to…

We propose a new algorithm for the optimization of convex functions over a polyhedral set in Rn. The algorithm extends the spectral projected-gradient method with limited-memory BFGS iterates restricted to the present face whenever…

Strong gravitational lensing offers a wealth of astrophysical information on the background source it affects, provided the lensed source can be reconstructed as if it was seen in the absence of lensing. In the present work, we illustrate…

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this…

Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and…

Convex optimization problems are common in hyperspectral unmixing. Examples include: the constrained least squares (CLS) and the fully constrained least squares (FCLS) problems, which are used to compute the fractional abundances in linear…

Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such as the space of Radon measures, are much less developed than in Hilbert spaces. Most numerical…

Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq…

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the…

Gravitational lens modeling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the…

This paper presents a sharp geometric analysis of the recovery performance of sparse regularization. More specifically, we analyze the BLASSO method which estimates a sparse measure (sum of Dirac masses) from randomized sub-sampled…

We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…

In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums. This…

Beurling LASSO generalizes the LASSO problem to finite Radon measures regularized via their total variation. Despite its theoretical appeal, this space is hard to parametrize, which poses an algorithmic challenge. We propose a formulation…

Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance…