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Recent breakthrough results in compressive sensing (CS) have established that many high dimensional signals can be accurately recovered from a relatively small number of non-adaptive linear observations, provided that the signals possess a…
In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as measurement matrix. The samples are subsequently forwarded to…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS…
The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in…
Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, the existing…
In this article, we address the problem of reducing the number of required samples for Spherical Near-Field Antenna Measurements (SNF) by using Compressed Sensing (CS). A condition to ensure the numerical performance of sparse recovery…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
We study compressed sensing (CS) signal reconstruction problems where an input signal is measured via matrix multiplication under additive white Gaussian noise. Our signals are assumed to be stationary and ergodic, but the input statistics…
Our objective is to efficiently design a robust projection matrix $\Phi$ for the Compressive Sensing (CS) systems when applied to the signals that are not exactly sparse. The optimal projection matrix is obtained by mainly minimizing the…
Compressive sensing is a novel approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate and outperforms traditional signal processing techniques in acquiring and reconstructing…
Compressed sensing has been a very successful high-dimensional signal acquisition and recovery technique that relies on linear operations. However, the actual measurements of signals have to be quantized before storing or processing.…
The recovery of sparse data is at the core of many applications in machine learning and signal processing. While such problems can be tackled using $\ell_1$-regularization as in the LASSO estimator and in the Basis Pursuit approach,…
In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
Oversampled adaptive sensing (OAS) is a recently proposed Bayesian framework which sequentially adapts the sensing basis. In OAS, estimation quality is, in each step, measured by conditional mean squared errors (MSEs), and the basis for the…
In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…
Joint sparsity has attracted considerable attention in recent years in many fields including sparse signal recovery in compressed sensing (CS), statistics, and machine learning. Traditional convex models suffer from the suboptimal…