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In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…
Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. While parameter…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…
In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…
In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…
A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the…
We consider the problem of recovering an $n_1 \times n_2$ low-rank matrix with $k$-sparse singular vectors from a small number of linear measurements (sketch). We propose a sketching scheme and an algorithm that can recover the singular…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…
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…
Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from…
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…
One-bit compressed sensing (1bCS) is a method of signal acquisition under extreme measurement quantization that gives important insights on the limits of signal compression and analog-to-digital conversion. The setting is also equivalent to…
We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x in R^n from the signs of O(s log^2(n/s)) random linear measurements…
The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for…
Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…
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,…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
In many linear inverse problems, we want to estimate an unknown vector belonging to a high-dimensional (or infinite-dimensional) space from few linear measurements. To overcome the ill-posed nature of such problems, we use a low-dimension…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…