Sparsity adaptive matching pursuit algorithm for practical compressed sensing

Abstract

This paper presents a novel iterative greedy reconstruction algorithm for practical compressed sensing (CS), called the sparsity adaptive matching pursuit (SAMP). Compared with other state-of-the-art greedy algorithms, the most innovative feature of the SAMP is its capability of signal reconstruction without prior information of the sparsity. This makes it a promising candidate for many practical applications when the number of non-zero (significant) coefficients of a signal is not available. The proposed algorithm adopts a similar flavor of the EM algorithm, which alternatively estimates the sparsity and the true support set of the target signals. In fact, SAMP provides a generalized greedy reconstruction framework in which the orthogonal matching pursuit and the subspace pursuit can be viewed as its special cases. Such a connection also gives us an intuitive justification of trade-offs between computational complexity and reconstruction performance. While the SAMP offers a comparably theoretical guarantees as the best optimization-based approach, simulation results show that it outperforms many existing iterative algorithms, especially for compressible signals.

Matching Pursuit for Sparse Signal Reconstruction Based on Dual Thresholds

“…For non-adaptive algorithms, the forward and backward stepsize areconstant K for SP, constant 2K for CoSaMP, as well as constant α and β for FBP. The adaptive algorithmswhose step size are variable include adaptive sparse matching pursuit (ASMP) [11], adaptive threshold backtracking orthogonal matching pursuit (ATBOMP) [12], and others similar algorithms [13], [14].…”

A Novel Approach for the Estimation of Doubly Spread Acoustic Channels Based on Wavelet Transform

“…From (12), the time shift is determined by both time delay and Doppler scale factor. So it is difficult to estimate a l and τ l simultaneously when only sending one HFM signal.…”

“…Hence only a few channel taps in MSML channel model are nonzero and need to be tracked. As a result, the computational complexity has been reduced and many sparse channel estimation algorithms based on compressed-sensing (CS) have been proposed [7,[10][11][12][13][14][15].…”

“…The traditional subspace methods and CS-based methods are compared in [7], and the author concludes that CS-based methods have better performances in channel estimation. Meanwhile, some improved algorithms, which focus on adaptively estimating path numbers, like sparsity adaptive matching pursuit (SaMP) [12] and adaptive step size SaMP (AS-SaMP) [13] have been applied to sparse channel estimation. Furthermore, some references propose methods to reduce computation: a two-stage OMP algorithm is proposed by [14], which estimates the Doppler scale factor and time delay respectively, rather than simultaneously as OMP does.…”

Learning with dynamic group sparsity

“…For example, we do not know the exact sparsity numbers of the background subtracted images although we know they tend to be dynamic group sparse. Motivated by the idea in [7], we develop a new recovery algorithm called AdaDGS by incorporating an adaptive sparsity scheme into the above DGS recovery algorithm.…”