In this paper we aim to solve a problem of image reconstruction in tomography. In medical imaging, patients suffer from taking high dose of radioactive drug in order to get a well-qualified image. Our goal is to reduce this dose of radioactive drug given to the patients in PET scan and to get a well-qualified image. We use to modeling this problem using a convex function to minimize. In tomography, real problem requires a positive constraint and may get a blurred image due to poisson noise. Then, in order to get back a non blurred image of human body, we add to this function a wavelet regularization which is a non differentiable function. We introduce specific algorithms to get the minimum of the global function obtained. After presenting the classic algorithms with their conditions to solve the problem we find that Chambolle Pock's algorithm requires less properties than these algorithms and gives good results. Then, we propose its computation method with the proof.