Robust blurred image recovery using minimax and semi-definite programming approaches

In this paper we propose novel approaches for robust blur removal and image reconstruction considering uncertainty in the blur kernel. The stochastic minimization approach models the kernel uncertainty as a stochastic spatial random process, while the worst case reconstruction is a robust minimax scheme which minimizes the maximum image distortion over a set of uncertainty blur kernels. The worst case minimization is demonstrated to be capable of image recovery employing knowledge of the nominal blur kernel matrix and uncertainty strength. Further, we also propose a semi-definite programming (SDP) based scheme for image recovery employing a linear matrix uncertainty model. Another key strength of the proposed schemes is that they can readily incorporate an L₁ norm based total variational cost, thereby resulting in significantly superior performance of image reconstruction. Simulation results show that our approach is able to recover the images with superior visual clarity and lower mean squared-error compared to conventional nominal kernel based non-robust image recovery approaches.