# Reverse image filtering using total derivative approximation and accelerated gradient descent

arXiv: https://arxiv.org/abs/2112.04121 · HTML: https://mlsanity.com/paper/2112.04121/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 50 references that are in the map.
- First posted on arXiv 8 Dec 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Polyblur: Removing mild blur by polynomial reblurring](https://mlsanity.com/paper/2012.09322/) (2020)
- [Zero-order Reverse Filtering](https://mlsanity.com/paper/1704.04037/) (2017)
- [Real-time Image Smoothing via Iterative Least Squares](https://mlsanity.com/paper/2003.07504/) (2020)
- [Rendition: Reclaiming what a black box takes away](https://mlsanity.com/paper/1804.08651/) (2018)
- [A guided edge-aware smoothing-sharpening filter based on patch interpolation model and generalized Gamma distribution](https://mlsanity.com/paper/2107.14765/) (2021)

## Abstract (arXiv)

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.