Simultaneous blur map estimation and deblurring of a single space-variantly defocused image

In this work we address the problem of blind deblurring using a single space-variantly defocused image containing text. We estimate both the all-in-focus image and the blur map corresponding to the space-variant point spread function of the finite aperture camera. Since this problem is highly ill-posed we exploit a recently proposed technique [1] to obtain an initial estimate of the space-variant blur map which is used in an MAP-MRF alternating minimization framework. We obtain analytically the gradients with respect to the unknowns and show that the proposed objective function can be successfully optimized with the steepest descent technique. Initially, we show results using the Gauss-Markov random field (GMRF) prior and then contrast its performance with the discontinuity adaptive Markov random field (DAMRF) prior. We show that details such as edges and fine details are preserved by the DAMRF regularizer. We compare the results of our algorithm with state-of-the-art techniques and provide both qualitative and quantitative evaluation.