Statistical prior based low complexity recovery for compressed image sensing

In this paper, a low complexity yet high performance recovery method coupling with the separable image sensing encoder is proposed, by exploring the statistical prior of image representations in the wavelet domain. Specifically, the energy distribution of natural images in the wavelet domain is investigated and found to be well characterized by an exponential decay model, which is then used as statistical priori information during the recovery algorithm design. The recovery process is composed of two steps, where the row-wise (or column-wise) intermediates and column-wise (or row-wise) final results are reconstructed sequentially. During each step of the recovery, the reconstruction is constrained to conform with the statistical prior by introducing a weight matrix. Two recovery strategies with different levels of complexity are designed, named the one-time direct recovery (OTD) and the two-times iterative recovery (TTI). The OTD strategy focuses on extremely fast recovery speed, with same weight matrixes for the two steps. While for the TTI strategy, the weight matrix for the second step will be iteratively refined, aiming to achieve more accurate recovery results. Extensive simulations have been conducted, and results show that the proposed recovery method with OTD strategy can achieve much faster recovery speed than traditional methods, and at the same time, the recovery quality is better; recovery with TTI strategy can achieve the best recovery quality at the expense of slight degradation in recovery speed, yet still faster than the traditional methods.