Abstract
Nonlinear sparse sensing (NSS) techniques have been adopted for realizing compressive sensing in many applications such as radar imaging. Unlike the NSS, in this paper, we propose an adaptive sparse sensing (ASS) approach using the reweighted zero-attracting normalized least mean fourth (RZA-NLMF) algorithm which depends on several given parameters, i.e., reweighted factor, regularization parameter, and initial step size. First, based on the independent assumption, Cramer-Rao lower bound (CRLB) is derived as for the performance comparisons. In addition, reweighted factor selection method is proposed for achieving robust estimation performance. Finally, to verify the algorithm, Monte Carlo-based computer simulations are given to show that the ASS achieves much better mean square error (MSE) performance than the NSS.
Highlights
Compressive sensing (CS) [1,2] has been attracting high attention in compressive radar/sonar sensing [3,4] due to its many applications such as civilian, military, and biomedical
The main task of CS problems can be divided into three aspects as follows: (1) sparse signal learning: The basic model suggests that natural signals can be compactly expressed, or efficiently approximated, as a linear combination of prespecified atom signals, where the linear coefficients are sparse as shown in Figure 1
It is well known that the CS provides a robust framework that can reduce the number of measurements required to estimate a sparse signal
Summary
Compressive sensing (CS) [1,2] has been attracting high attention in compressive radar/sonar sensing [3,4] due to its many applications such as civilian, military, and biomedical. Many nonlinear sparse sensing (NSS) algorithms and their variants have been proposed to deal with CS problems. They mainly fall into two basic categories: convex relaxation (basis pursuit de-noise (BPDN) [6]) and greedy pursuit (orthogonal matching pursuit (OMP) [7]). We propose an adaptive sparse sensing (ASS) method using the reweighted zero-attracting normalized mean fourth error algorithm (RZA-NLMF) [8] to solve the CS problems. Different from NSS methods, each observation and corresponding sensing signal vector will be implemented by the RZA-NLMF algorithm to reconstruct the sparse signal during the process of adaptive filtering. From the perspective of CS, the sensing matrix X satisfies the restricted isometry property (RIP) in overwhelming probability [5] so that the sparse signal h can be reconstructed correctly by NSS methods, e.g., BPDN [6] and OMP [7]. 4n−6μiss σ ð27Þ evaluated by average mean square error (MSE) which is defined by Average
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