Fast iterative reverse filters using fixed-point acceleration

Abstract

Iterative reverse filters have been recently developed to address the problem of removing effects of a black box image filter. Because numerous iterations are usually required to achieve the desired result, the processing speed is slow. In this paper, we propose to use fixed-point acceleration techniques to tackle this problem. We present an interpretation of existing reverse filters as fixed-point iterations and discuss their relationship with gradient descent. We then present extensive experimental results to demonstrate the performance of fixed-point acceleration techniques named after: Anderson, Chebyshev, Irons, and Wynn. We also compare the performance of these techniques with that of gradient descent acceleration. Key findings of this work include: (1) Anderson acceleration can make a non-convergent reverse filter convergent, (2) the T-method with an acceleration technique is highly efficient and effective, and (3) in terms of processing speed, all reverse filters can benefit from one of the acceleration techniques.