An algorithm for image reconstruction based on lp norm

Abstract

Image reconstruction is one of the key technologies in the fields of physical imaging, which include optical imaging, photoacoustic imaging, sonar imaging, magnetic resonance imaging, and celestial imaging etc. Compressive sensing theory, the new research spot in recent years, describes that a small group of non-adaptive linear projections of a sparse or compressible signal contains enough information for signal reconstruction. Compressive sensing has been applied in many physical imaging systems. In this paper, we propose a new image reconstruction algorithm based on lp norm compressive sensing by combining the penalty function and revised Hesse sequence quadratic programming, and using block compressive sensing. Several images, such as “cameraman”, “barbara” and “mandrill”, are chosen as the images for image reconstruction. First, we take different sampling rates for image reconstruction to verify the algorithm. When the sampling rate is as low as 0.3, the signal-to-noise ratio of the reconstructed image can reach up to 32.23 dB. Then, when the sampling rate is above 0.5, by comparing with OMP algorithm, reconstructed images can be obtained with a higher signal-to-noise ratio and a shorter imaging time. Especially, when the sampling rate is 0.7, the imaging time is reduced by 88%. Finally compared with the existing algorithm based on lp norm compressive sensing, simulation results show that the new algorithm can improve the signal-to-noise ratio of reconstructed images, and greatly reduce the imaging time.