Efficient Block-sparse Signal Recovery with Application to ECG Compression

Abstract

Compressed sensing enables sparse signals recovery from few linear measurements. For many types of signals, such as those which exhibit sparsity in the wavelet domain, the non-zero elements occur in blocks. Signals of this type are referred to as block-sparse signals. This paper proposes a block-sparse signal reconstruction algorithm, block adaptive matching pursuit (BAMP), which is characterized by high speed and accuracy. In this algorithm, a number of blocks is selected in each iteration, which is adapted according to the average correlation between the signal and blocks of the measurement matrix. Moreover, in each iteration, the support is refined, or pruned, to exclude blocks that do not contribute to the signal. We apply BAMP to ECG signal recovery from compressed measurements. Simulations illustrate significant improvements in accuracy and speed in comparison to other related block-sparse recovery algorithms for random and ECG signals.