# F2former: When Fractional Fourier Meets Deep Wiener Deconvolution and Selective Frequency Transformer for Image Deblurring

arXiv: https://arxiv.org/abs/2409.02056 · HTML: https://mlsanity.com/paper/2409.02056/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 57 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Builds on (most cited first, 30 of 30)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Uformer: A General U-Shaped Transformer for Image Restoration](https://mlsanity.com/paper/2106.03106/) (2021)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [Selective Kernel Networks](https://mlsanity.com/paper/1903.06586/) (2019)
- [Rethinking Coarse-to-Fine Approach in Single Image Deblurring](https://mlsanity.com/paper/2108.05054/) (2021)
- [Deep Stacked Hierarchical Multi-patch Network for Image Deblurring](https://mlsanity.com/paper/1904.03468/) (2019)
- [Deblurring by Realistic Blurring](https://mlsanity.com/paper/2004.01860/) (2020)
- [Human-Aware Motion Deblurring](https://mlsanity.com/paper/2001.06816/) (2020)
- [Efficient Frequency Domain-based Transformers for High-Quality Image Deblurring](https://mlsanity.com/paper/2211.12250/) (2022)
- [Efficient and Explicit Modelling of Image Hierarchies for Image Restoration](https://mlsanity.com/paper/2303.00748/) (2023)
- [Defocus Deblurring Using Dual-Pixel Data](https://mlsanity.com/paper/2005.00305/) (2020)
- [Multi-class Token Transformer for Weakly Supervised Semantic Segmentation](https://mlsanity.com/paper/2203.02891/) (2022)
- [Multi-Temporal Recurrent Neural Networks For Progressive Non-Uniform Single Image Deblurring With Incremental Temporal Training](https://mlsanity.com/paper/1911.07410/) (2019)
- [Iterative Filter Adaptive Network for Single Image Defocus Deblurring](https://mlsanity.com/paper/2108.13610/) (2021)
- [Intriguing Findings of Frequency Selection for Image Deblurring](https://mlsanity.com/paper/2111.11745/) (2021)
- [Single Image Defocus Deblurring Using Kernel-Sharing Parallel Atrous Convolutions](https://mlsanity.com/paper/2108.09108/) (2021)
- [Learning to Reduce Defocus Blur by Realistically Modeling Dual-Pixel Data](https://mlsanity.com/paper/2012.03255/) (2020)
- [AdaRevD: Adaptive Patch Exiting Reversible Decoder Pushes the Limit of Image Deblurring](https://mlsanity.com/paper/2406.09135/) (2024)
- [Towards Robust, Locally Linear Deep Networks](https://mlsanity.com/paper/1907.03207/) (2019)
- [Phase-only Image Based Kernel Estimation for Single-image Blind Deblurring](https://mlsanity.com/paper/1811.10185/) (2018)
- [Y-net: Multi-scale feature aggregation network with wavelet structure similarity loss function for single image dehazing](https://mlsanity.com/paper/2003.13912/) (2020)
- [Revisiting Image Deblurring with an Efficient ConvNet](https://mlsanity.com/paper/2302.02234/) (2023)
- [INFWIDE: Image and Feature Space Wiener Deconvolution Network for Non-blind Image Deblurring in Low-Light Conditions](https://mlsanity.com/paper/2207.08201/) (2022)
- [Microscopy Image Restoration with Deep Wiener-Kolmogorov filters](https://mlsanity.com/paper/1911.10989/) (2019)

## Built on by (most cited first, 2 of 2)

- [NTIRE 2025 Challenge on Day and Night Raindrop Removal for Dual-Focused Images: Methods and Results](https://mlsanity.com/paper/2504.12711/) (2025)
- [Leveraging Diffusion Knowledge for Generative Image Compression with Fractal Frequency-Aware Band Learning](https://mlsanity.com/paper/2503.11321/) (2025)

## Abstract (arXiv)

Recent progress in image deblurring techniques focuses mainly on operating in both frequency and spatial domains using the Fourier transform (FT) properties. However, their performance is limited due to the dependency of FT on stationary signals and its lack of capability to extract spatial-frequency properties. In this paper, we propose a novel approach based on the Fractional Fourier Transform (FRFT), a unified spatial-frequency representation leveraging both spatial and frequency components simultaneously, making it ideal for processing non-stationary signals like images. Specifically, we introduce a Fractional Fourier Transformer (F2former), where we combine the classical fractional Fourier based Wiener deconvolution (F2WD) as well as a multi-branch encoder-decoder transformer based on a new fractional frequency aware transformer block (F2TB). We design F2TB consisting of a fractional frequency aware self-attention (F2SA) to estimate element-wise product attention based on important frequency components and a novel feed-forward network based on frequency division multiplexing (FM-FFN) to refine high and low frequency features separately for efficient latent clear image restoration. Experimental results for the cases of both motion deblurring as well as defocus deblurring show that the performance of our proposed method is superior to other state-of-the-art (SOTA) approaches.