title: Model-assisted adaptive recovery of compressed sensing with imaging applications.
abstract: In compressive sensing (CS), a challenge is to find a space in which the signal is sparse and, hence, faithfully recoverable. Since many natural signals such as images have locally varying statistics, the sparse space varies in time/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 framework for model-guided adaptive recovery of compressive sensing (MARX) and show how a 2-D piecewise autoregressive model can be integrated into the MARX framework to make CS recovery adaptive to spatially varying second order statistics of an image. In addition, MARX offers a mechanism of characterizing and exploiting structured sparsities of natural images, greatly restricting the CS solution space. Simulation results over a wide range of natural images show that the proposed MARX technique can improve the reconstruction quality of existing CS methods by 2-7 dB.
authors.affiliation: Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada. xwu@ece.mcmaster.ca
authors.forename: Xiaolin
authors.initials: X
authors.lastname: Wu
authors.forename: Weisheng
authors.initials: W
authors.lastname: Dong
authors.forename: Xiangjun
authors.initials: X
authors.lastname: Zhang
authors.forename: Guangming
authors.initials: G
authors.lastname: Shi