Abstract
In recent years, various applications regarding sparse continuous signal recovery such as source localization, radar imaging, communication channel estimation, etc., have been addressed from the perspective of compressive sensing (CS) theory. However, there are two major defects that need to be tackled when considering any practical utilization. The first issue is off-grid problem caused by the basis mismatch between arbitrary located unknowns and the pre-specified dictionary, which would make conventional CS reconstruction methods degrade considerably. The second important issue is the urgent demand for low-complexity algorithms, especially when faced with the requirement of real-time implementation. In this paper, to deal with these two problems, we have presented three fast and accurate sparse reconstruction algorithms, termed as HR-DCD, Hlog-DCD and Hlp-DCD, which are based on homotopy, dichotomous coordinate descent (DCD) iterations and non-convex regularizations, by combining with the grid refinement technique. Experimental results are provided to demonstrate the effectiveness of the proposed algorithms and related analysis.
Highlights
Compressive sensing (CS) and sparse signal representation have received widespread attention and increasing interest over the past few years [1,2], which are motivated by the sparse nature of the real world data and the advantages of the CS theory
It is worth noting that there may be other factors leading to basis mismatch, for example, in the radar imaging field, unsatisfactory system parameters are likely to degrade the performance of conventional CS-based methods from our previous researches, this paper only focuses on the off-grid problem, and assumes the system errors are small enough
In order to reduce the complexity of the dichotomous coordinate descent (DCD) algorithm, we develop a greedy algorithm that is based on homotopy method with respect to a set of the parameter
Summary
Compressive sensing (CS) and sparse signal representation have received widespread attention and increasing interest over the past few years [1,2], which are motivated by the sparse nature of the real world data and the advantages of the CS theory. The applications of CS in numerous areas have been widely investigated in the literature, such as magnetic resonance imaging (MRI) [3], synthetic aperture radar (SAR) imaging [4], inverse synthetic aperture radar (ISAR) imaging [5], passive radar imaging [6], direction-of-arrival (DOA) estimation [7], communication channel estimation [8], seismic signal processing [9], spectral estimation [10], image processing [11], speech enhancement [12], etc. The above equation is usually ill-posed, the CS theory has shown that if satisfies some certain conditions, we can construct and stably from highly undersampled measurements [14]
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