Greedy algorithms are popular in compressive sensing for their high computational efficiency. But the performance of current greedy algorithms can be degenerated seriously by noise (both multiplicative noise and additive noise). A robust version of greedy cosparse greedy algorithm (greedy analysis pursuit) is presented in this paper. Comparing with previous methods, The proposed robust greedy analysis pursuit algorithm is based on an optimization model which allows both multiplicative noise and additive noise in the data fitting constraint. Besides, a new stopping criterion that is derived. The new algorithm is applied to compressive sensing of ECG signals. Numerical experiments based on real-life ECG signals demonstrate the performance improvement of the proposed greedy algorithms.
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