  A framework of online adaptive statistical compressed sensing is introduced
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 measurements. For signals generated from a Gaussian mixture model, the
online adaptive sensing algorithm is given and its performance is analyzed. 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 random measurements, at a marginally
increased computational complexity.
