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Rapid Gradient Projection Algorithm for Image Reconstruction

In order to improve the speed of compressed sensing image reconstruction algorithm, a rapid gradient projection algorithm for image reconstruction is proposed. In traditional Gradient Projection algorithm, the pursuit direction is alternating, in rapid gradient projection algorithm, we use the Newton's method to calculate the gradient descent direction, thus the constraints conditions of gradient projection is satisfied. And the target function is updated in each iteration computing. The effect of approximation matrix to target function is reduced. The iteration computing times is reduced, because the algorithm works in accurate search direction. Experiment results show that, compared with the GPSR algorithm, the RGPSR algorithm improves the signals reconstruction accuracy, improves PSNR of reconstruction signals, and exhibits higher robustness under different noise intensities.