Related papers: Sparse sampling recovery by greedy algorithms
Local-search methods are widely employed in statistical applications, yet interestingly, their theoretical foundations remain rather underexplored, compared to other classes of estimators such as low-degree polynomials and spectral methods.…
Compressive sampling has great potential for making wideband spectrum sensing possible at sub-Nyquist sampling rates. As a result, there have recently been research efforts that leverage compressive sampling to enable efficient wideband…
It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…
In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted $\ell_1$ minimization over that sparsity model. In particular, we focus on a model where the entries of the unknown vector fall into…
We discuss two new methods of recovery of sparse signals from noisy observation based on $\ell_1$- minimization. They are closely related to the well-known techniques such as Lasso and Dantzig Selector. However, these estimators come with…
In this paper, we consider the "foreach" sparse recovery problem with failure probability $p$. The goal of which is to design a distribution over $m \times N$ matrices $\Phi$ and a decoding algorithm $\algo$ such that for every…
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 a novel greedy algorithm for the support recovery of a sparse signal from a small number of noisy measurements. In the proposed method, a new support index is identified for each iteration based on bit-wise maximum a posteriori…
In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In…
Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, numerical solution of symmetric positive definite linear…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…
A robust algorithm is proposed to reconstruct the spatial support and the Lam\'e parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of…
We formulate sparse support recovery as a salient set identification problem and use information-theoretic analyses to characterize the recovery performance and sample complexity. We consider a very general model where we are not restricted…
Sparsity is one of the key concepts that allows the recovery of signals that are subsampled at a rate significantly lower than required by the Nyquist-Shannon sampling theorem. Our proposed framework uses arbitrary multiscale transforms,…
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…
We propose and analyze a weighted greedy scheme for computing deterministic sample configurations in multidimensional space for performing least-squares polynomial approximations on $L^2$ spaces weighted by a probability density function.…
We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…
We consider machine learning techniques to develop low-latency approximate solutions to a class of inverse problems. More precisely, we use a probabilistic approach for the problem of recovering sparse stochastic signals that are members of…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by…