Patch-Based Image Processing alternating direction methods of multipliers (ADMM)

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Hi everyone I meet a problem recently, which is about image processing. The application is image reconstruction.

Originally I want to use ADMM to solve the pixel-based problem which involves gradient and Laplacian matrix. But I find that patch-based image processing is more suitable for image reconstruction.

Therefore, I want to modify the original problem into patch-based one. That is, I divide the original problem into several patches. And then implement ADMM for each patch in parallel. Finally convert the resulting blocks into a big picture.

But I dont know whether this is practicable. Is parallel ADMM for each patch better than pixel-based ADMM? Could anyone provide some suggestions? Thanks in advance!