Fast Image Deconvolution using Hyper-Laplacian Priors

This document is supplementary material to our NIPS 2009 paper [1] of the same name. While we choose to solve the w sub-problem (Eqn. 5) in [1] using a LUT or analytically (for some specific values of α), a number of numerical alternatives exist. The simplest and fastest approach is to use Newton-Raphson (NR) to find the roots of the polynomials in Eqn. 10 and Eqn 11 of [1]. As shown in Table 1, 4 iterations of NR take a similar time to our analytic solution. However, the numerical algorithm has poor stability, particularly when the polynomials skim the x-axis. In practice, we found it gave spurious solutions around 1-2 % of the time, an unacceptable rate given the iterative nature of our overall algorithm.…