An Approach to 2D Signals Recovering in Compressive Sensing Context

Abstract

In this paper we study the compressive sensing effects on 2D signals exhibiting sparsity in 2D DFT domain. A simple algorithm for reconstruction of randomly under-sampled data is proposed. It is based on the analytically determined threshold that precisely separates signal and non-signal components in the 2D DFT domain. The algorithm operates fast in a single iteration providing the accurate signal reconstruction. In the situations that are not comprised by the analytic derivation and constrains, the algorithm is still efficient and need just a couple of iterations. The proposed solution shows promising results in ISAR imaging (simulated data are used), where the reconstruction is achieved even in the case when less than 10% of data is available.

A Modified Compressed Sensing-Based Recovery Algorithm for Wireless Sensor Networks

“…Specifically, the sensed signals are measured by Gaussian random matrices Φ j ∈ R M x ×400 in each time instant τ = 31 s, and the sink received the measured signals. The simulation results are reported from the obtained mean results of 100 frames with different x j s. The performance of the proposed reconstruction algorithm is compared with gradient-CS [11], SFAR-2D [12], reweightedlaplace [13], sequential-CS [20], modified-CS [29] and regularized modified-BPDN [30]. During the simulation, several parameters of the algorithms have been carefully tuned to perform an impartial comparison between the algorithms.…”

“…And as the number of measurements increases, the performance of the methods gradually approaches that of the proposed algorithm. The reconstruction times versus different measurement numbers for gradient-CS [11], SFAR-2D [12], reweighted-laplace [13], sequential-CS [20], modified-CS [29], regularized modified-BPDN [30] and the proposed algorithm is depicted in Fig. 2.…”

“…Due to the main challenges of the energy constraint WSNs, reducing the overall energy consumption of the sensor nodes is of great importance. In this respect, compressive sensing (CS) has drawn much interest, simultaneously providing a sensing and compression framework [1][2][3][4][5][6][7][8][9], enabling a potentially significant reduction in the sampling and computational costs of a sensor with limited capabilities; while still guaranteeing perfect recovery [10][11][12][13]. Although CS has established a promising performance in exploiting the spatial or temporal correlation, the necessary data transmission can be decreased more.…”

Tensor-based Match Pursuit Algorithm for MIMO Radar Imaging

“…In order to effectively explain the proposed algorithm superiority, standard OMP and SP are presented at the same time. Gradient algorithm for ISAR proposed in [18] and a new 2D signals recovering algorithm proposed in [19] are presented at the same time to compare with the TMP algorithm. From Fig.…”

On some common compressive sensing recovery algorithms and applications

“…where ℑ ℑ ℑ ℑ denotes 2D DFT matrix obtained as a Kronecker product of two I×J DFT matrices: Reconstruction of 2D signals -SFAR 2D [96]). The algorithm is tested on the simulated radar signal.…”