Related papers: Sparse polynomial interpolation: sparse recovery, …
Finding the sparse representation of a signal in an overcomplete dictionary has attracted a lot of attention over the past years. This paper studies ProSparse, a new polynomial complexity algorithm that solves the sparse representation…
In this paper, we solve the l2-l1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and apply a limited-memory trust-region method. Unlike gradient projection-type…
In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type". These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics, such as…
Deep learning techniques have been successfully applied in many areas of computer vision, including low-level image restoration problems. For image super-resolution, several models based on deep neural networks have been recently proposed…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
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 transforms. Our key…
Consider the regularized sparse minimization problem, which involves empirical sums of loss functions for $n$ data points (each of dimension $d$) and a nonconvex sparsity penalty. We prove that finding an…
The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to…
Existing approaches to compressive sensing of frequency-sparse signals focuses on signal recovery rather than spectral estimation. Furthermore, the recovery performance is limited by the coherence of the required sparsity dictionaries and…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…
The reconstruction of a high resolution image given a low resolution observation is an ill-posed inverse problem in imaging. Deep learning methods rely on training data to learn an end-to-end mapping from a low-resolution input to a…
This article analyzes the recovery performance of two popular finite dimensional approximations of the sparse spikes deconvolution problem over Radon measures. We examine in a unified framework both the L1 regularization (often referred to…
Inspired by the robustness and efficiency of sparse representation in sparse coding based image restoration models, we investigate the sparsity of neurons in deep networks. Our method structurally enforces sparsity constraints upon hidden…
In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal…
Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…
We consider a convex relaxation of sparse principal component analysis proposed by d'Aspremont et al. in (d'Aspremont et al. SIAM Rev 49:434-448, 2007). This convex relaxation is a nonsmooth semidefinite programming problem in which the…
Based on the computation of a superset of the implicit support, implicitization of a parametrically given hyper-surface is reduced to computing the nullspace of a numeric matrix. Our approach exploits the sparseness of the given parametric…