Related papers: Analysis of Regularized LS Reconstruction and Rand…
This paper proposes a compressed sensing (CS) framework for the acquisition and reconstruction of frequency-sparse signals with chaotic dynamical systems. The sparse signal is acting as an excitation term of a discrete-time chaotic system…
Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based…
Reconstructing a signal on a graph from noisy observations of a subset of the vertices is a fundamental problem in the field of graph signal processing. This paper investigates how sample size affects reconstruction error in the presence of…
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…
In this paper, we endeavor for predicting the performance of quantized compressive sensing under the use of sparse reconstruction estimators. We assume that a high rate vector quantizer is used to encode the noisy compressive sensing…
As one of the recently proposed algorithms for sparse system identification, $l_0$ norm constraint Least Mean Square ($l_0$-LMS) algorithm modifies the cost function of the traditional method with a penalty of tap-weight sparsity. The…
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…
Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…
Compressed sensing of sparse sources can be improved by incorporating prior knowledge of the source. In this paper we demonstrate a method for optimal selection of weights in weighted $L_1$ norm minimization for a noiseless reconstruction…
The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
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…
Compressed sensing (CS) involves sampling signals at rates less than their Nyquist rates and attempting to reconstruct them after sample acquisition. Most such algorithms have parameters, for example the regularization parameter in LASSO,…
This work proposes an adaptive trace lasso regularized L1-norm based graph cut method for dimensionality reduction of Hyperspectral images, called as `Trace Lasso-L1 Graph Cut' (TL-L1GC). The underlying idea of this method is to generate…
This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…
The Lasso is a popular regression method for high-dimensional problems in which the number of parameters $\theta_1,\dots,\theta_N$, is larger than the number $n$ of samples: $N>n$. A useful heuristics relates the statistical properties of…
Compressed sensing is an important problem in many fields of science and engineering. It reconstructs signals by finding sparse solutions to underdetermined linear equations. In this work we propose a deterministic and non-parametric…
We construct two families of deterministic sensing matrices where the columns are obtained by exponentiating codewords in the quaternary Delsarte-Goethals code $DG(m,r)$. This method of construction results in sensing matrices with low…
We consider rank-one symmetric tensor estimation when the tensor is corrupted by Gaussian noise and the spike forming the tensor is a structured signal coming from a generalized linear model. The latter is a mathematically tractable model…
$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many…