Recovering the Blur Kernel from Natural Image Statistics: An Analysis of the Goldstein-Fattal Method
Jérémy Anger, Gabriele Facciolo, Mauricio Delbracio
⚠ This is a preprint. It may change before it is accepted for publication.


Despite the significant improvement in image quality mainly caused by the improvement in optical sensors and general electronics, blur due to camera shake significantly undermines the quality of hand-held photographs being one of the most active research topics. In this work, we present a detailed description and implementation of the blurring kernel estimation algorithm introduced by Goldstein and Fattal in 2012. Unlike most methods that attempt to solve an inverse problem through a variational formulation (e.g., through a maximum a posteriori estimation), this method directly estimates the blurring kernel by modeling statistical irregu- larities in the power spectrum of blurred natural images. The adopted mathematical model extends the well-known power-law by contemplating the presence of dominant strong edges in particular directions. The blurring kernel is retrieved from an estimation of the blurring kernel power spectrum, by solving a phase retrieval problem using additional constraints due to the particular nature of camera shake blurring kernels (e.g., non-negativity and small spatial support). Although the algorithm is conceptually simple, being based on several clean mathematical/physical assumptions, the numerical implementation presents several challenges. This work contributes to a detailed anatomy of the Goldstein and Fattal method, and the algorithms that constitute it and its parameters.