Deterministic constructions of compressed sensing matrices
Journal of Complexity
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
On verifiable sufficient conditions for sparse signal recovery via ℓ 1 minimization
Mathematical Programming: Series A and B - Special Issue on "Optimization and Machine learning"; Alexandre d’Aspremont • Francis Bach • Inderjit S. Dhillon • Bin Yu
Optimization with Sparsity-Inducing Penalties
Foundations and Trends® in Machine Learning
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
On sparse representations in arbitrary redundant bases
IEEE Transactions on Information Theory
Recovery of exact sparse representations in the presence of bounded noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
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The paper deals with the estimation of the maximal sparsity degree for which a given measurement matrix allows sparse reconstruction through ℓ1-minimization. This problem is a key issue in different applications featuring particular types of measurement matrices, as for instance in the framework of tomography with low number of views. In this framework, while the exact bound is NP hard to compute, most classical criteria guarantee lower bounds that are numerically too pessimistic. In order to achieve an accurate estimation, we propose an efficient greedy algorithm that provides an upper bound for this maximal sparsity. Based on polytope theory, the algorithm consists in finding sparse vectors that cannot be recovered by ℓ1-minimization. Moreover, in order to deal with noisy measurements, theoretical conditions leading to a more restrictive but reasonable bounds are investigated. Numerical results are presented for discrete versions of tomography measurement matrices, which are stacked Radon transforms corresponding to different tomograph views.