Coherence pattern-guided compressive sensing with unresolved grids Highly coherent sensing matrices arise in discretization of continuum imaging problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold. Algorithms based on techniques of band exclusion (BE) and local optimization (LO) are proposed to deal with such coherent sensing matrices. These techniques are embedded in the existing compressed sensing algorithms, such as orthogonal matching pursuit (OMP), subspace pursuit (SP), iterative hard thresholding (IHT), basis pursuit (BP), and Lasso, and result in the modified algorithms BLOOMP, BLOSP, BLOIHT, BP-BLOT, and Lasso-BLOT, respectively. Under appropriate conditions, it is proved that BLOOMP can reconstruct sparse, widely separated objects up to one Rayleigh length in the Bottleneck distance independent of the grid spacing. One of the most distinguishing attributes of BLOOMP is its capability of dealing with large dynamic ranges. par The BLO-based algorithms are systematically tested with respect to four performance metrics: dynamic range, noise stability, sparsity, and resolution. With respect to dynamic range and noise stability, BLOOMP is the best performer. With respect to sparsity, BLOOMP is the best performer for high dynamic range, while for dynamic range near unity BP-BLOT and Lasso-BLOT with the optimized regularization parameter have the best performance. In the noiseless case, BP-BLOT has the highest resolving power up to certain dynamic range. The algorithms BLOSP and BLOIHT are good alternatives to BLOOMP and BP/Lasso-BLOT: they are faster than both BLOOMP and BP/Lasso-BLOT and share, to a lesser degree, BLOOMP’s amazing attribute with respect to dynamic range. Detailed comparisons with the algorithms spectral iterative hard thresholding and the frame-adapted BP demonstrate the superiority of the BLO-based algorithms for the problem of sparse approximation in terms of highly coherent, redundant dictionaries.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 16 articles , 1 standard article )

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  1. Lou, Yifei; Yan, Ming: Fast L1-L2 minimization via a proximal operator (2018)
  2. Zhang, Shuai; Xin, Jack: Minimization of transformed $L_1$ penalty: theory, difference of convex function algorithm, and robust application in compressed sensing (2018)
  3. Ma, Tian-Hui; Lou, Yifei; Huang, Ting-Zhu: Truncated $l_1-2$ models for sparse recovery and rank minimization (2017)
  4. Wang, Dan; Zhang, Zhuhong: Generalized sparse recovery model and its neural dynamical optimization method for compressed sensing (2017)
  5. Yang, Zai; Xie, Lihua: On gridless sparse methods for multi-snapshot direction of arrival estimation (2017)
  6. Zhu, Zhihui; Wakin, Michael B.: Approximating sampled sinusoids and multiband signals using multiband modulated DPSS dictionaries (2017)
  7. Adcock, Ben; Hansen, Anders C.: Generalized sampling and infinite-dimensional compressed sensing (2016)
  8. Cai, T. Tony; Eldar, Yonina C.; Li, Xiaodong: Global testing against sparse alternatives in time-frequency analysis (2016)
  9. Liao, Wenjing; Fannjiang, Albert: MUSIC for single-snapshot spectral estimation: stability and super-resolution (2016)
  10. Lou, Yifei; Yin, Penghang; Xin, Jack: Point source super-resolution via non-convex $L_1$ based methods (2016)
  11. Duval, Vincent; Peyré, Gabriel: Exact support recovery for sparse spikes deconvolution (2015)
  12. Lou, Yifei; Yin, Penghang; He, Qi; Xin, Jack: Computing sparse representation in a highly coherent dictionary based on difference of $L_1$ and $L_2$ (2015)
  13. Yin, Penghang; Lou, Yifei; He, Qi; Xin, Jack: Minimization of $\ell_1-2$ for compressed sensing (2015)
  14. Chen, Guangliang; Divekar, Atul; Needell, Deanna: Guaranteed sparse signal recovery with highly coherent sensing matrices (2014)
  15. Strohmer, Thomas; Friedlander, Benjamin: Analysis of sparse MIMO radar (2014)
  16. Fannjiang, Albert; Liao, Wenjing: Coherence pattern-guided compressive sensing with unresolved grids (2012)