Reverse image filtering using total derivative approximation and accelerated gradient descent
This addresses the challenge of undoing image filters without prior knowledge of the algorithm, which is incremental but improves efficiency and applicability for image processing tasks.
The paper tackles the problem of reversing unknown image filters by formulating it as a minimization problem using total derivative approximation and gradient descent, achieving results that outperform state-of-the-art methods in terms of complexity and the number of reversible filters.
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.