Sparse Signal Representation, Sampling, and Recovery in Compressive Sensing Frameworks

Abstract

Compressive sensing allows the reconstruction of original signals from a much smaller number of samples as compared to the Nyquist sampling rate. The effectiveness of compressive sensing motivated the researchers for its deployment in a variety of application areas. The use of an efficient sampling matrix for high-performance recovery algorithms improves the performance of the compressive sensing framework significantly. This paper presents the underlying concepts of compressive sensing as well as previous work done in targeted domains in accordance with the various application areas. To develop prospects within the available functional blocks of compressive sensing frameworks, a diverse range of application areas are investigated. The three fundamental elements of a compressive sensing framework (signal sparsity, subsampling, and reconstruction) are thoroughly reviewed in this work by becoming acquainted with the key research gaps previously identified by the research community. Similarly, the basic mathematical formulation is used to outline some primary performance evaluation metrics for 1D and 2D compressive sensing.

An Enhanced Subsampling Technique in Compressive Sensing using Linear Interpolation and Random Measurement Matrix

“…incoherence is absolutely assured. Since efficient signal reconstruction in CS is highly dependent on incoherence [4,24], we can conclude that on the incoherence feature, our proposed technique outweighs a state-the-art ones like Wei's [9] and subsampling by random measurement.…”

“…In some papers, it is either the case that the relevance of the incoherence of a measurement matrix required for subsampling is watered down like in [6], or as observed in [5] the subsampling techniques largely proposed for signal reconstruction still have an implicit significant probability of coherence within the sensing matrix, with an insufficient theoretical framework to provide certainty of a successful CS method. In [4] and [12] The rest of the paper is organized as follows;…”

“…The underdetermined CS problem as stated in [4][5][6][7] and also explained earlier, was formulated in MATLAB as follows:…”

“…While sparsity refers to when a signal (matrix) has fewer non-zero entries than zero entries [3], incoherence has to do with the requirement that measurements of the original signal taken need to evenly represent random sections of the given signal. More precisely, as mathematically presented in the CS problem stated in [4][5][6][7], and subsequently in this paper, the measurement matrix, Φ, should not be parallel with the columns of the transform basis matrix, Ψ, such that it only subsamples signals from those columns at the expense of the other columns [3]. What incoherence aims at is to have randomness with measurements taken from a signal to increase the efficiency of its reconstruction.…”

Recovery performance improvement of image compressive sensing using complex‐valued Vandermonde matrix

“…The compressive sensing (CS) theory states that if a signal is sparse or compressible, it can be sampled below the Nyquist rate at the transmission side, while it can be reconstructed with these samples of the signal at the receiver side [1,2]. CS has been applied to various areas such as wireless communication [3], image signal processing [4,5], wireless sensor networks [6] etc.…”