An image reconstruction algorithm based on compressed sensing using conjugate gradient

A new image reconstruction algorithm based on compressed sensing using conjugate gradient is proposed for the first time in this paper. Compressed sensing is a technique for acquiring and reconstructing a signal or image utilizing the prior knowledge that is sparse or compressible. During the past several decades scholars have made all sorts of guesses about the prior Pr(x) for images in order to find its sparse representation and also proposed some available algorithms like matching pursuit (MP) and orthogonal matching pursuit (OMP) algorithms. Some reconstruction algorithms used the convex relaxation method, but the conjugate gradient is a method with simpler iterative process and less memory requirement compared with the least square and Newton iteration. Simulation results show that this image reconstruction algorithm based on compressed sensing using conjugate gradient gets better performance on time and PSNR than OMP algorithm.