A fractional-order regularization with sparsity constraint for blind restoration of images

Blind image deconvolution is one of the most challenging problems in image restoration. Inspired by the work on sparsity constraint and deblurring of blind motion, we propose a model with fractional-order regularization and sparsity constraint for blind restoration and construct split Bregman combining an iterative thresholding algorithm. Fractional-order penalty term Bqβ(Lp(Ω))(0<β≤1) in Besov space is expanded by wavelet basis and computed using iterative thresholding algorithm. The regularized terms of blur kernel under tight wavelet frame systems are solved by the split Bregman method. Numerical experiments show that our algorithm can effectively remove different kinds of blur without requiring any prior information of the blur kernels and obtain higher signal-to-noise ratios and lower relative errors. In addition, fractional-order derivative in Besov space can preserve both edges and smoothness better than the integer-order derivative.