In An asymptotic result on compressed sensing matrices [4], a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we analyse the performance of these matrices using deterministic and probabilistic methods. We provide a new recovery algorithm and detailed simulations. These simulations suggest that the construction is competitive with...

In this paper, we propose a general framework for the asymptotic analysis of node-based verification-based algorithms. In our analysis we tend the signal length n to infinity. We also let the number of non-zero elements of the signal k scale linearly with n. Using the proposed framework, we study the asymptotic behavior of the recovery algorithms over random sparse matrices (graphs) in the cont...

In this paper, we apply distributed compressive sensing (DCS) in heterogeneous sensor network (HSN). Combining different types of measurement matrices and different numbers of measurements, we firstly investigate three different scenarios in which HSN is used for signal acquisition. In the first scenario, there are two different types of measurement matrices. One is Gaussian measurement and the...

In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable to natural non-Gaussian distributions without further assumptions, as can be demonstrated by simple counter-examples involving extremely sparse signals. We s...

Compressive hyperspectral imaging is based on the fact that hyperspectral data is highly redundant. However, there is no symmetry between the compressibility of the spatial and spectral domains, and that should be taken into account for optimal compressive hyperspectral imaging system design. Here we present a study of the influence of the ratio between the compression in the spatial and spectr...

The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this literature, the structure is represented by sparsity in a well-chosen basis. We show how to achieve guarantees similar to standard compressed sensing but without emp...

Abstract. A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani and Sochen. In this paper, we first revisit closed formulae of the finite split oscillator dictionary S by a simple proof. Then we study the non-split tori of the group SL(2, Fp). Finally, An explicit algorithm for computing the finite non...

We proposed a weighted l minimization: min , ‖x‖ + λ‖f‖ s.t.Ax+ f= b to recover a sparse vector x and the corrupted noise vector f from a linear measurement b = Ax + f when the sensing matrix A is an m × n row i.i.d subgaussian matrix. Our first result shows that the recovery is possible when the fraction of corrupted noise is smaller than a positive constant, provided that ‖x‖ ≤ O(n/ln (n/‖x ∗...

We develop methods to efficiently reconstruct the topology and line parameters of a power grid from the measurement of nodal variables. We propose two compressed sensing algorithms that minimize the amount of necessary measurement resources by exploiting network sparsity, symmetry of connections and potential prior knowledge about the connectivity. The algorithms are reciprocal to established s...