Here is the result (click the picture for large view):
The pink dashed line is the performance curve of the method. The errors in the first few snapshots are obviously reduced, compared to the performance curve of the method that performing MSBL on the whole data (indicated by the red solid line).
Obviously, MMV algorithms can be applied to dynamic compressed sensing problems in this block on-line style. In the above experiment MSBL stepped by 10 snapshots. Here are more experiment results when MSBL stepped by 2, 3 and 5 snapshots (for comparison, I also plotted the results of KF-CS,KF-Genie, LS-CS, and MSBL applied on the whole data from the above experiment):
Z. Zhang, B.D.Rao, Exploiting Correlation in Sparse Signal Recovery Problems: Multiple Measurement Vectors, Block Sparsity, and Time-Varying Sparsity, ICML 2011 Workshop on Structured Sparsity