Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Scientific Computing
Deterministic constructions of compressed sensing matrices
Journal of Complexity
Toeplitz-Structured Compressed Sensing Matrices
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Compressed Sensing and Redundant Dictionaries
IEEE Transactions on Information Theory
Nonlinear image recovery with half-quadratic regularization
IEEE Transactions on Image Processing
Information Sciences: an International Journal
Unsupervised images segmentation via incremental dictionary learning based sparse representation
Information Sciences: an International Journal
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The emerging theory of compressive or compressed sensing challenges the convention of modern digital signal processing by establishing that exact signal reconstruction is possible for many problems where the sampling rate falls well below the Nyquist limit. Following the landmark works of Candès et al. and Donoho on the performance of l1-minimization models for signal reconstruction, several authors demonstrated that certain nonconvex reconstruction models consistently outperform the convex l1-model in practice at very low sampling rates despite the fact that no global minimum can be theoretically guaranteed. Nevertheless, there has been little theoretical investigation into the performance of these nonconvex models. In this paper, a notion of weak signal recoverability is introduced and the performance of nonconvex reconstruction models employing general concave metric priors is investigated under this model. The sufficient conditions for establishing weak signal recoverability are shown to substantially relax as the prior functional is parameterized to more closely resemble the targeted l0-model, offering new insight into the empirical performance of this general class of reconstruction methods. Examples of relaxation trends are shown for several different prior models.