  In this paper, we study the problem of reverse image filtering. An image
filter denoted g(.), which is available as a black box, produces an observation
b = g(x) when provided with an input x. The problem is to estimate the original
input signal x from the black box filter g(.) and the observation b. We study
and re-develop state-of-the-art methods from two points of view, fixed point
iteration and gradient descent. We also explore the application of acceleration
techniques for the two types of iterations. Through extensive experiments and
comparison, we show that acceleration methods for both fixed point iteration
and gradient descent help to speed up the convergence of state-of-the-art
methods.
