Generalized best-first search strategies and the optimality of A*
Journal of the ACM (JACM)
Statistical methods for speech recognition
Statistical methods for speech recognition
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Incremental heuristic search in AI
AI Magazine
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
A plurality of sparse representations is better than the sparsest one alone
IEEE Transactions on Information Theory
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
Sublinear compressive sensing reconstruction via belief propagation decoding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Decoding by linear programming
IEEE Transactions on Information Theory
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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Compressed sensing is a developing field aiming at the reconstruction of sparse signals acquired in reduced dimensions, which make the recovery process under-determined. The required solution is the one with minimum @?"0 norm due to sparsity, however it is not practical to solve the @?"0 minimization problem. Commonly used techniques include @?"1 minimization, such as Basis Pursuit (BP) and greedy pursuit algorithms such as Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP). This manuscript proposes a novel semi-greedy recovery approach, namely A* Orthogonal Matching Pursuit (A*OMP). A*OMP performs A* search to look for the sparsest solution on a tree whose paths grow similar to the Orthogonal Matching Pursuit (OMP) algorithm. Paths on the tree are evaluated according to a cost function, which should compensate for different path lengths. For this purpose, three different auxiliary structures are defined, including novel dynamic ones. A*OMP also incorporates pruning techniques which enable practical applications of the algorithm. Moreover, the adjustable search parameters provide means for a complexity-accuracy trade-off. We demonstrate the reconstruction ability of the proposed scheme on both synthetically generated data and images using Gaussian and Bernoulli observation matrices, where A*OMP yields less reconstruction error and higher exact recovery frequency than BP, OMP and SP. Results also indicate that novel dynamic cost functions provide improved results as compared to a conventional choice.