Model-Guided Adaptive Recovery of Compressive Sensing

For the new signal acquisition methodology of compressive sensing (CS) a challenge is to find a space in which the signal is sparse and hence recoverable faithfully. Given the nonstationarity of many natural signals such as images, the sparse space is varying in time or spatial domain. As such, CS recovery should be conducted in locally adaptive, signal-dependent spaces to counter the fact that the CS measurements are global and irrespective of signal structures. On the contrary existing CS reconstruction methods use a fixed set of bases (e.g., wavelets, DCT, and gradient spaces) for the entirety of a signal. To rectify this problem we propose a new model-based framework to facilitate the use of adaptive bases in CS recovery. In a case study we integrate a piecewise stationary autoregressive model into the recovery process for CS-coded images, and are able to increase the reconstruction quality by $2 \thicksim 7$dB over existing methods. The new CS recovery framework can readily incorporate prior knowledge to boost reconstruction quality.