An Improved Bregman Iterative Algorithm

Image processing is an important area of scientific research. Some basic elements of image processing, such as the geometry of the image processing, image enhance-ment, as well as rehabilitation. etc, are from image to image, that is, the original data is input image, the output is still image, but image reconstruction is from the data to the image. Image reconstruction has been widely applied in astronomy, geology, remote sensing, computer, communications, radar, medical imaging and other important areas. In the signal restoration and image reconstruction, rehabilitation and reconstruction of sparse data has become a hotspot, that is, in the premise of the image quality, we try to use a small amount of data recovery or reconstruction.Firstly, the history and current situation of signal and image reconstruction tech-nology development, some properties and applications of compressed sensing theory, medical image reconstruction, the background and significance of signal and image re-construction, and the recent status is briefly reviewed. We will research lp minimization problem where x∈Rn indicated the reconstructed image, A∈Rm×n said sensor matrix, b∈Rn indicated that the data is scaned by the imaging device.Generally, we translate lp minimization problem (1.5) into l2-lp minimization problem (1.6) to solve. where Aλ∈(0,∞). We list some algorithms of solving l2-lp minimization problem (1.6), and analyze the advantages and disadvantages of these algorithms, some deficiencies of the algorithms is mainly caused by non-Lipschitz continuity of the lp norm. Bregman iterative algorithm requires the objective function is convex, while lp norm is not con-vex, so we need to change it into convex function. To speed up the computational speed, we add the iterations of the parameterμto Bregman iterative algorithm, and prove the convergence of the algorithm, that is, a sequence of solutions which is generated by the algorithm in a limited iteration converges to the optimal solution of lp minimization problem.