Related papers: Recovery algorithms for vector valued data with jo…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
We studied linear weighted sampling algorithms and their optimality for approximate recovery of functions with mixed smoothness on $\mathbb{R}^d$ from a set of $n$ their sampled values. Functions to be recovered are in weighted Sobolev…
In this paper, we develop verifiable and computable performance analysis of sparsity recovery. We define a family of goodness measures for arbitrary sensing matrices as a set of optimization problems, and design algorithms with a…
Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…
We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…
We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood,…
This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…
This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient…
We propose novel algorithms that enhance the performance of recovering unknown continuous-valued frequencies from undersampled signals. Our iterative reweighted frequency recovery algorithms employ the support knowledge gained from earlier…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted $\ell_{2,1}$ ($\mathit{ow}\ell_{2,1}$), which is specifically designed to take…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
We consider two problems that arise in machine learning applications: the problem of recovering a planted sparse vector in a random linear subspace and the problem of decomposing a random low-rank overcomplete 3-tensor. For both problems,…
The stability of sparse signal reconstruction is investigated in this paper. We design efficient algorithms to verify the sufficient condition for unique $\ell_1$ sparse recovery. One of our algorithm produces comparable results with the…
Recovery of sparse vectors and low-rank matrices from a small number of linear measurements is well-known to be possible under various model assumptions on the measurements. The key requirement on the measurement matrices is typically the…
Sparse subspace clustering (SSC) relies on sparse regression for accurate neighbor identification. Inspired by recent progress in compressive sensing, this paper proposes a new sparse regression scheme for SSC via two-step reweighted…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing.…
Recovering latent structure from count data has received considerable attention in network inference, particularly when one seeks both cross-group interactions and within-group similarity patterns in bipartite networks, which is widely used…
A new sparse signal recovery algorithm for multiple-measurement vectors (MMV) problem is proposed in this paper. The sparse representation is iteratively drawn based on the idea of zero-point attracting projection (ZAP). In each iteration,…