Reverse image filtering using total derivative approximation and accelerated gradient descent

TL;DR

This paper introduces a novel method for reversing unknown image filters using total derivative approximation and accelerated gradient descent, achieving superior efficiency and effectiveness compared to existing techniques.

Contribution

It proposes a new inverse filtering algorithm that handles unknown, black-box filters with improved speed and reversibility, utilizing total derivatives and accelerated gradient methods.

Findings

Outperforms state-of-the-art reverse filters in complexity and reversibility.

Effectively reverses a larger set of filters with lower computational cost.

Demonstrates robustness and efficiency through extensive experiments.

Abstract

In this paper, we address a new problem of reversing the effect of an image filter, which can be linear or nonlinear. The assumption is that the algorithm of the filter is unknown and the filter is available as a black box. We formulate this inverse problem as minimizing a local patch-based cost function and use total derivative to approximate the gradient which is used in gradient descent to solve the problem. We analyze factors affecting the convergence and quality of the output in the Fourier domain. We also study the application of accelerated gradient descent algorithms in three gradient-free reverse filters, including the one proposed in this paper. We present results from extensive experiments to evaluate the complexity and effectiveness of the proposed algorithm. Results demonstrate that the proposed algorithm outperforms the state-of-the-art in that (1) it is at the same level of complexity as that of the fastest reverse filter, but it can reverse a larger number of filters, and (2) it can reverse the same list of filters as that of the very complex reverse filter, but its complexity is much smaller.