Abstract
Cosparse analysis model (CAM) provides a new signal processing paradigm for recovering cosparse signals with respect to a given analysis operator from the undersampled linear measurements in the context of emerging theory of compressed sensing (CS). The sparse analysis recovery/cosparse recovery is a key one brought up by this new paradigm. In this paper, we propose a new family of analysis pursuit algorithms for the sparse analysis recovery problem when the signals obey the cosparse analysis model, termed as iterative cosupport detection estimation (ICDE). ICDE is an algorithmic framework, which alternates between detecting a cosupport set of the unknown true signal and estimating the underlying signal by solving a truncated analysis pursuit problem on the detected cosupport. Further, we propose effective implementations of ICDE equipped with an efficient thresholding strategy for cosupport detection. Empirical performance comparisons show that ICDE is favorable in comparison with the state-of-the-art sparse analysis recovery algorithms. Source code of ICDE has been made publicly available on Github: https://github.com/songhp/ICDE.
Highlights
Data models for sparsity-exploiting applications in image and signal processing have drawn much attention in last decade [1], [2]
Motivated by the aforementioned works, we develop a general class of analysis pursuit algorithms, termed iterative cosupport detection-estimation (ICDE), attempting to provide analysis versions of the synthesis counterpart algorithms
EXPERIMENTAL RESULTS we carry out comparative experiments with greedy analysis pursuit (GAP), analysis basis pursuit (ABP) and Analysis SP (ASP), which some of the experiments performed in [3], [29] for both synthetic and real-world datasets
Summary
Data models for sparsity-exploiting applications in image and signal processing have drawn much attention in last decade [1], [2]. The sparse synthesis model (SSM) [3] offers an elegant approach to lead the era of sparse representation [4]–[8]. In this model, the unknown signal x ∈ Rd of interest can be represented as a linear combination of some atoms of fixed matrix D (column vectors). The mathematical model of SSM can be denoted as x = Dz, where D ∈ Rd×n is a overcomplete dictionary (d ≤ n), and z ∈ Rn is the sparse representation of signal x. The support is the index set of non-zero coefficients of z, which synthesize the signal x from atoms of D. Song et al.: Sparse Analysis Recovery via ICDE (CoSaMP) [15], hard thresholding pursuit (HTP) [16] and recent work [17]
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