TITLE:
Compressive Sensing Algorithms for Signal Processing Applications: A Survey
AUTHORS:
Mohammed M. Abo-Zahhad, Aziza I. Hussein, Abdelfatah M. Mohamed
KEYWORDS:
Compressive Sensing, Shannon Sampling Theory, Sensing Matrices, Sparsity, Coherence
JOURNAL NAME:
International Journal of Communications, Network and System Sciences,
Vol.8 No.6,
June
9,
2015
ABSTRACT: In digital signal processing (DSP),
Nyquistrate sampling completely describes a signal by exploiting its
bandlimitedness. Compressed Sensing (CS), also known as compressive sampling,
is a DSP technique efficiently acquiring and reconstructing a signal completely
from reduced number of measurements, by exploiting its compressibility. The
measurements are not point samples but more general linear functions of the
signal. CS can capture and represent sparse signals at a rate significantly
lower than ordinarily used in the Shannon’s sampling theorem. It is interesting
to notice that most signals in reality are sparse; especially when they are
represented in some domain (such as the wavelet domain) where many coefficients
are close to or equal to zero. A signal is called K-sparse, if it can be
exactly represented by a basis, , and a set of coefficients , where only K
coefficients are nonzero. A signal is called approximately K-sparse, if it can
be represented up to a certain accuracy using K non-zero coefficients. As an
example, a K-sparse signal is the class of signals that are the sum of K
sinusoids chosen from the N harmonics of the observed time interval. Taking the
DFT of any such signal would render only K non-zero values . An example of
approximately sparse signals is when the coefficients , sorted by magnitude,
decrease following a power law. In this case the sparse approximation
constructed by choosing the K largest coefficients is guaranteed to have an
approximation error that decreases with the same power law as the coefficients.
The main limitation of CS-based systems is that they are employing iterative
algorithms to recover the signal. The sealgorithms are slow and the hardware
solution has become crucial for higher performance and speed. This technique
enables fewer data samples than traditionally required when capturing a signal
with relatively high bandwidth, but a low information rate. As a main feature
of CS, efficient algorithms such as -minimization can be used for recovery.
This paper gives a survey of both theoretical and numerical aspects of
compressive sensing technique and its applications. The theory of CS has many
potential applications in signal processing, wireless communication,
cognitive radio and medical imaging.
