# Zero-order Reverse Filtering

arXiv: https://arxiv.org/abs/1704.04037 · HTML: https://mlsanity.com/paper/1704.04037/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2017.

## Built on by (most cited first, 8 of 8)

- [Deep Posterior Distribution-based Embedding for Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2205.14887/) (2022)
- [Panchromatic and Multispectral Image Fusion via Alternating Reverse Filtering Network](https://mlsanity.com/paper/2210.08181/) (2022)
- [SONIC: Spectral Optimization of Noise for Inpainting with Consistency](https://mlsanity.com/paper/2511.19985/) (2025)
- [FlowOpt: Fast Optimization Through Whole Flow Processes for Training-Free Editing](https://mlsanity.com/paper/2510.22010/) (2025)
- [Geometric and Learning-based Mesh Denoising: A Comprehensive Survey](https://mlsanity.com/paper/2209.00841/) (2022)
- [Metropolis Theorem and Its Applications in Single Image Detail Enhancement](https://mlsanity.com/paper/2302.09762/) (2023)
- [Reverse image filtering using total derivative approximation and accelerated gradient descent](https://mlsanity.com/paper/2112.04121/) (2021)
- [SPICE: Simple and Practical Image Clarification and Enhancement](https://mlsanity.com/paper/2510.08358/) (2025)

## Abstract (arXiv)

In this paper, we study an unconventional but practically meaningful reversibility problem of commonly used image filters. We broadly define filters as operations to smooth images or to produce layers via global or local algorithms. And we raise the intriguingly problem if they are reservable to the status before filtering. To answer it, we present a novel strategy to understand general filter via contraction mappings on a metric space. A very simple yet effective zero-order algorithm is proposed. It is able to practically reverse most filters with low computational cost. We present quite a few experiments in the paper and supplementary file to thoroughly verify its performance. This method can also be generalized to solve other inverse problems and enables new applications.