Recovery of correlated sparse signals using adaptive backtracking matching pursuit

In distributed compressive sensing, if one signal in a joint-sparse signal ensemble is known apriori, the remaining signals can be reconstructed using modified Compressive Sensing (CS) algorithms such as Modified Basis Pursuit (Mod-BP) which makes use of Partially Known Support (PKS). Though Mod-BP reconstructs the joint-sparse signals with high accuracy, it takes a huge amount of time to converge. This might not be desirable in some practical applications like CS reconstruction of video frames. Carrillo et al have illustrated the use of PKS in iterative greedy algorithms to improve the recovery performance at a much shorter time. However, PKS based iterative greedy algorithms are totally blind about the wrong atoms present in the PKS, which is likely for video frames. To overcome this, we propose Adaptive Backtracking Matching Pursuit (AdBMP) which makes effective use of the PKS to reconstruct the sparse signal. Experimental results show that AdBMP gives a better reconstruction accuracy compared to that of the existing PKS based iterative greedy algorithms.