Image deblurring with mixed regularization via the alternating direction method of multipliers

In image deblurring problems, both local and nonlocal regularization priors are well studied. Local regularization prior assumes piecewise smoothness and transform-based sparsity, while the nonlocal one exploits self-similarity of images. We proposed a mixed regularization model which incorporates the advantages of both local adaptive sparsity prior and nonlocal sparsity prior resulting from the nonlocal self-similarity, and thus encourages a solution to simultaneously express both the local and nonlocal natures of images. The deblurring problem with mixed regularization can be transformed into a constrained optimization problem with separable structure via the variable splitting. Then this constrained optimization problem is solved by the alternating direction method of multipliers. Experimental results with a set of images under varying conditions demonstrate that the proposed method achieves the state-of-the-art deblurring performance. (C) 2015 SPIE and IS&T