Task-driven adaptive statistical compressive sensing of gaussian mixture models

A framework of online adaptive statistical compressed sensing is in-troduced for signals following a mixture model. The scheme first uses non-adaptive measurements, from which an online decoding scheme estimates the model selection. As soon as a candidate model has been selected, an optimal sensing scheme for the selected model continues to apply. The final signal reconstruction is calculated from the ensemble of both the non-adaptive and the adaptive measure-ments. For signals generated from a Gaussian mixture model, the online adaptive sensing algorithm is given and its performance is an-alyzed. On both synthetic and real image data, the proposed adaptive scheme considerably reduces the average reconstruction error with respect to standard statistical compressed sensing that uses fully ran-dom measurements, at a marginally increased computational com-plexity. Index Terms — Statistical compressed sensing, adaptive sensing, Gaussian mixture models, model selection. 1