An Image Reconstruction Model under Poisson Noise Using multiscale Compressed Sensing

Abstract

For the influence of poisson noise images, in order to get rid of poisson noise, this paper put forward image reconstruction method by using multiscale compressed sensing. the algorithm can approximate the optimal sparse representation of the image edge details such as the characteristics of theShearlet domain based multi-scale compressed sensing method. The image is decomposed into the high-frequency subbands byShearlet, and the compressed sensing is applied into each subband to reconstruct the image. In this paper, A total variation of RL iterative algorithm constructed by nonlinear projection algorithm based on closed convex set is explored as the reconstruction method, which use derivation of the nonlinear projection instead of total variation. In mathematics, Shearlet has been proved to be a better tool for edge characterization than traditional wavelet. By using the nonlinear projection scheme to constrain the residual coefficients in the Shearlet domain, a better estimation can be obtained from the Shearlet representation. Numerical examples show that the denoising effect of these methods is very good, which is better than the correlation method based on Curvelet transform. In addition, the number of iterations required by our scheme is far less than that of our competitors.