Parallel linearized ADMM with application to multichannel image restoration and reconstruction

Many large-scale regularized inverse problems in imaging such as image restoration and reconstruction can be modeled as a generic objective function involves sum of nonsmooth but proximable terms, which are usually linear-operator-coupled. For the solution of these problems, a parallel linearized alternating direction method of multipliers (PLADMM) is proposed in this paper. At each step of the proposed algorithm, the proximity operators of the nondifferential terms are called individually. This leads to a highly parallel algorithm structure, where most sub-steps can be simultaneously solved. Profiting from the linearization step, the linear inverse operation is excluded. The convergence property of the proposed method is analyzed. The image deblurring, inpainting, and pMRI reconstruction experiments show that the proposed method has vast applicable vistas. Compared with the state-of-the-art methods, such as PADMM [21], FTVD-v4 [22], PPDS [33], FUSL [8], LADM [36], and ALADMM [27], it gains competitive results both in terms of quantitative indicators, such as PSNR or SSIM, and in terms of visual impression.