Sparsity Adaptive Matching Pursuit Algorithm for Practical Compressed Sensing
JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
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This paper presents a novel iterative greedy reconstruction algorithm for practical compressed sensing CS, called the sparsity adaptive matching pursuit SAMP. Compared with other state-of-the-art greedy algorithms, the most innovative feature of the SAMP is its capability of signal reconstruction without prior information of the sparsity. This makes it a promising candidate for many practical applications when the number of non-zero significant coefficients of a signal is not available. The proposed algorithm adopts a similar flavor of the EM algorithm, which alternatively estimates the sparsity and the true support set of the target signals. In fact, SAMP provides a generalized greedy reconstruction framework in which the orthogonal matching pursuit and the subspace pursuit can be viewed as its special cases. Such a connection also gives us an intuitive justification of trade-offs between computational complexity and reconstruction performance. While the SAMP offers a comparably theoretical guarantees as the best optimization-based approach simulation results show that it outperforms many existing iterative algorithms, especially for compressible signals.
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