  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.
