An MDL-based multi-task classification and reconstruction algorithm

In the multi-task compressive sensing (MCS) algorithm, multi-task specifically denotes the set of different compressive measurements. The MCS algorithm can utilize all tasks together to reconstruct original signals and its reconstruction performance outperforms that of the single-task compressive sensing algorithm. However, when the original signals belong to different clusters (it means that the original signals in every cluster have similar structure), we can not utilize all tasks together to reconstruct original signals, and should make signal reconstruction after classifying the tasks. In view of this problem, we propose a minimum description length (MDL) principle based multi-task classification and reconstruction algorithm. First, we establish the classification principle of the multi-task reconstruction algorithm, by which we can obtain the number of clusters. Then, the multi-task reconstruction algorithm is carried out for every cluster respectively. Example results demonstrate the better classification and reconstruction performance of the proposed method compared to other algorithms.