Iterative gradient projection algorithm for two-dimensional compressive sensing sparse image reconstruction

The basic theories and techniques in compressive sensing (CS) are established on the sampling and reconstruction of one-dimensional (1D) signals. When it is applied to two-dimensional (2D) images, the images are first stacked in a large vector. However, this vectorization not only destroys the spatial structure of the 2D image, but also increases computational complexity and memory requirements. As a result, some researchers proposed the concept of 2D CS. The major challenge of 2D CS is to design a reconstruction algorithm that can directly reconstruct the 2D image data from the 2D random projection. In this paper, a 2D CS sparse image reconstruction algorithm based on iterative gradient projection is proposed. In the proposed algorithm, the sparse solution is searched iteratively in the 2D solution space and then updated by gradient descent of the total variation (TV) and bivariate shrinkage in the dual-tree discrete wavelet transform (DDWT) domain. Numerous experiments are performed on several natural images. Compared with several state-of-the-art reconstruction algorithms, the proposed algorithm is more efficient and robust, not only yielding higher peak-signal-to-noise ratio but also reconstructing images of better subjective visual quality.