Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
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Compressive sampling (CS) is aimed at acquiring a signal or image from data which is deemed insufficient by Nyquist/Shannon sampling theorem. Its main idea is to recover a signal from limited measurements by exploring the prior knowledge that the signal is sparse or compressible in some domain. In this paper, we propose a CS approach using a new total-variation measure TVL1, or equivalently TVl1, which enforces the sparsity and the directional continuity in the gradient domain. Our TVl1 based CS is characterized by the following attributes. First, by minimizing the l1-norm of partial gradients, it can achieve greater accuracy than the widely-used TVl1l2 based CS. Second, it, named hybrid CS, combines low-resolution sampling (LRS) and random sampling (RS), which is motivated by our induction that these two sampling methods are complementary. Finally, our theoretical and experimental results demonstrate that our hybrid CS using TVl1 yields sharper and more accurate images.