Choosing analysis or synthesis recovery for sparse reconstruction

The analysis sparsity model is a recently introduced alternative to the standard synthesis sparsity model frequently used in signal processing. However, the exact conditions when analysis-based recovery is better than synthesis recovery are still not known. This paper constitutes an initial investigation into determining when one model is better than the other, under similar conditions. We perform separate analysis and synthesis recovery on a large number of randomly generated signals that are simultaneously sparse in both models and we compare the average reconstruction errors with both recovery methods. The results show that analysis-based recovery is the better option for a large number of signals, but it is less robust with signals that are only approximately sparse or when fewer measurements are available.