One sketch for all: fast algorithms for compressed sensing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
Shifting inequality and recovery of sparse signals
IEEE Transactions on Signal Processing
Coherence analysis of iterative thresholding algorithms
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
CoSaMP: iterative signal recovery from incomplete and inaccurate samples
Communications of the ACM
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Decoding by linear programming
IEEE Transactions on Information Theory
Accelerated iterative hard thresholding
Signal Processing
Fast k-selection algorithms for graphics processing units
Journal of Experimental Algorithmics (JEA)
Sparsity lower bounds for dimensionality reducing maps
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
An efficient construction of reduced deformable objects
ACM Transactions on Graphics (TOG)
Matrix Recipes for Hard Thresholding Methods
Journal of Mathematical Imaging and Vision
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We introduce a new iterative algorithm to find sparse solutions of underdetermined linear systems. The algorithm, a simple combination of the Iterative Hard Thresholding algorithm and the Compressive Sampling Matching Pursuit algorithm, is called Hard Thresholding Pursuit. We study its general convergence and notice in particular that only a finite number of iterations are required. We then show that, under a certain condition on the restricted isometry constant of the matrix of the linear system, the Hard Thresholding Pursuit algorithm indeed finds all $s$-sparse solutions. This condition, which reads $\delta_{3 s}