Based on statistical prior information of image representations in the wavelet domain, we propose a low-complexity high-performance recovery method coupled with a separable image sensing encoder. By analyzing energy distribution of natural images in the wavelet domain, we develop an exponential decay model and use it as statisticalprior information in the algorithm. Particularly, the recovery process is composed of two steps, in which row-wise (or column-wise) intermediates and column-wise (or row-wise) final results are reconstructed sequentially. In each step, reconstruction is constrained to conform to the statistical prior by introducing a weight matrix. For different applications, we present two recovery strategies with different levels of complexity, namely one-time direct (OTD) recovery strategy and two-times iterative (TTI) recovery strategy. With OTD, the same weight matrix is used in both recovery steps to boost the recovery speed, whereas with TTI, the weight matrix in the second step is iteratively refined to enhance accuracy of recovery. Simulation results show that, compared to the traditional method, the proposed method boosts performance of compressed sensing recovery. In particular, the method with OTD can achieve much faster recovery speed and better recovery quality. Meanwhile, the best recovery quality can be obtained with TTI at the expense of slightly lowered recovery speed, yet still faster than traditional methods.
