Convergence analysis of a quadratic upper bounded TV regularizer based blind deconvolution

We provide a novel Fourier domain convergence analysis for blind deconvolution using the quadratic upper-bounded total variation (TV) as the regularizer. Though quadratic upper-bounded TV leads to a linear system in each step of the alternate minimization (AM) algorithm used, it is shift-variant, which makes Fourier domain analysis impossible. So we use an approximation which makes the system shift invariant at each iteration. The resultant points of convergence are better - in the sense of reflecting the data - than those obtained using a quadratic regularizer. We analyze the error due to the approximation used to make the system shift invariant. This analysis provides an insight into how TV regularization works and why it is better than the quadratic smoothness regularizer.