Compressive Sensing Image Reconstruction Based on Multiple Regulation Constraints.

Compressive sensing has emerged as a promising technique for signal processing. Most of the existing reconstruction methods cannot describe the sparsity of an image in different transform domains simultaneously, which results in an instability performance for images. In this paper, a new model based on compressive sensing is developed to describe the sparsity of an image in different transform domains simultaneously. The parameters of the a priori regularization terms, including the structural redundant information of wavelet coefficient, gradient coefficient and nonlocal mean, are adjusted adaptively to balance the influence of each corresponding constraint in the model. Some approximate substitutions are introduced to reduce the computational complexity. In addition, a two-step solution is proposed, in which an approximate image is reconstructed rapidly by picking parts of the constraints of the model. Then, an enhanced reconstruction performance can be achieved by adding the constraint of nonlocal mean. Simulation results demonstrate that the proposed method provides better performance in both peak signal-to-noise ratio and visual quality with a relatively fast convergence rate, especially at the low sample ratio. [ABSTRACT FROM AUTHOR]