Multi-task signal recovery by higher level hyper-parameter sharing

Sharing of hyper-parameters is often useful for multi-task problems as a means of encoding some notion of task similarity. Here we present a multi-task approach for signal recovery by sharing higher-level hyper-parameters which do not relate directly to the actual content of the signals of interest but only to their statistical characteristics. Our approach leads to a very simple model and algorithm that can be used to simultaneously recover multiple natural images with unrelated content. We investigate the advantages of this approach in relation to state of the art multi-task compressed sensing and we discuss our findings.