Applications Of ADMM Type Algorithms In Reconstruction Of Two Signals

Sparse signal denoising is widely used in compressed sensing,medical imaging,face recognition and other fields.With the progress of scientific technology and the develop-ment of society,we have entered the information age,people obtain information mainly through digital signals.When we make full and reasonable use of the data with rele-vance and redundancy,sparsity plays a vital role.Therefore,the research of sparse signal reconstruction algorithms has important theoretical significance and application value.In this paper,we discuss sparse signal reconstruction based on ADMM type algo-rithms.The main contents are as follows:1.We employ the weighted l₁-norm for sparsity induction function and propose the weighted l₁-norm minimization constraint model.The convergence of the algorithm is proved under proper assumptions.We do numerical experiments on 3D color images with salt noise,salt and pepper noise,and the results are used for comparing with JP algorithm and YALL1 algorithm.The PSNR and Rel Err of experimental results show that our algorithm has good restoration effect.2.We use the weighted l_q-norm(0?q<1)as sparse induction function.We solve the non-convex penalty model proposed by Wen et al by using the s PADMM algorithm.Under appropriate assumptions,it is proved that the iterative sequence converges to the KKT point of our problem,we do numerical experiments on 3D color images with salt noise and compare the s PADMM algorithm with JP algorithm,YALL1 algorithm and ADMM algorithm in reference[1].The experimental results show that our method is preferable in view of PSNR and Rel Err.