Total variation minimizing blind deconvolution with shock filter reference

We present a preconditioned method for blind image deconvolution. This method uses a pre-processed reference image (via the shock filter) as an initial condition for total variation minimizing blind deconvolution. Using the shock filter gives good information on location of the edges, while using the variational functionals such as Chan and Wong’s [T.F. Chan, C.K. Wong, Total variation blind deconvolution, IEEE Transactions on Image Processing 7 (1998), 370–375] allows robust reconstruction of the image and the blur kernel. Comparison between using the L1 and L2 norms for the fidelity term is presented, as well as an analysis on the choice of the parameter for the kernel functional. Numerical results indicate the method is robust for both black and non-black background images while reducing the overall computational cost.