FiRe: Fixed-Point Iteration for Image Restoration

Matthieu Terris, Ulugbek S. Kamilov, Thomas Moreau.

This repository contains the official implementation of our CVPR 2025 paper "FiRe: Fixed-Point Iteration for Image Restoration". This work introduces a novel approach to image restoration from the viewpoint of fixed-point iteration.

Features

The core idea of this work is to observe that, given a restoration model $\text{R}$ associated to a degradation operator $D$, the operator $\text{R}\circ D$ is an implicit prior of the form $x - \nabla \log p(x)$. In turns, this allows do derive new PnP-like algorithms that can be used to solve inverse problems.

Given a measurement $y = Ax + e$, where $A$ is a linear operator, $e$ is the realisation of some random noise, and $x$ is the image to restore, define $f(x) = \frac{1}{2} |Ax - y|^2$ as the data fidelity term. Then, if $\text{R}$ is a restoration model, we can define the fixed-point iteration associated to $\text{R}$ as

we can define the following algorithm:

$$\begin{align*} &u_k = (1-\gamma) x_k + \gamma \text{R}(x_{k}) \\\ &x_{k+1} = \text{prox}_{\lambda f}(u_k) \\\ \end{align*}$$

where $\gamma$ is a step size, and $\lambda$ is a regularization parameter.

Code

To reproduce the experiments, first download the test datasets and place them in your data folder. Next, update the config/config.json file to point to the correct data folder. There, there are two folders to specify:

• ROOT_DATASET: the folder within which the CBSD68 and set3c datasets are located;
• ROOT_CKPT: the path to the folder containing the pre-trained models.

Then, you can run the following scripts to reproduce the experiments:

Single restoration prior

python run_baselines.py --problem='gaussian_blur' --method_name='GD_swinir_2x' --dataset_name='set3c' --noise_level=0.01 --sigma_noise_max=0.01 --max_iter=60 --lambd=50 --eq=0

Motion deblurring prior (click to expand)

python run_baselines.py --problem='gaussian_blur' --method_name='GD_restormer_motion' --dataset_name='set3c' --noise_level=0.01 --l_value=0.6 --sigma_blur_value=1. --max_iter=60 --gamma=0.5 --motion_sigma_noise=0.005 --lambd=50 --eq=1 --results_folder='results_single_prior/'
python run_baselines.py --problem='motion_blur' --method_name='GD_restormer_motion' --dataset_name='set3c' --noise_level=0.01 --l_value=0.6 --sigma_blur_value=1. --max_iter=60 --gamma=1.0 --motion_sigma_noise=0.005 --lambd=20 --eq=1 --results_folder='results_single_prior/'
python run_baselines.py --problem='SRx4' --method_name='GD_restormer_motion' --dataset_name='set3c' --noise_level=0.01 --l_value=0.6 --sigma_blur_value=1. --max_iter=60 --gamma=1.0 --motion_sigma_noise=0.005 --lambd=50 --eq=1 --results_folder='results_single_prior/'

Gaussian deblurring prior (click to expand)

python run_baselines.py --problem='gaussian_blur' --method_name='GD_restormer_gaussian' --dataset_name='set3c' --noise_level=0.01 --sigma_blur_min=0.01 --sigma_blur_max=3.0 --max_iter=60 --gamma=1.0 --motion_sigma_noise=0.005 --lambd=20 --results_folder='results_single_prior/'
python run_baselines.py --problem='motion_blur' --method_name='GD_restormer_gaussian' --dataset_name='set3c' --noise_level=0.01 --sigma_blur_min=0.01 --sigma_blur_max=1.0 --max_iter=60 --gamma=1.0 --motion_sigma_noise=0.05 --lambd=20 --results_folder='results_single_prior/'
python run_baselines.py --problem='SRx4' --method_name='GD_restormer_gaussian' --dataset_name='set3c' --noise_level=0.01 --sigma_blur_min=0.01 --sigma_blur_max=4.0 --max_iter=60 --gamma=1.0 --motion_sigma_noise=0.02 --lambd=20 --results_folder='results_single_prior/'

Super resolution x2 / x3 prior (click to expand)

For SRx2:

python run_baselines.py --problem='gaussian_blur' --method_name='GD_swinir_2x' --dataset_name='set3c' --noise_level=0.01 --sigma_noise_max=0.01 --max_iter=60 --lambd=50 --eq=0 --results_folder='results_single_prior/'
python run_baselines.py --problem='motion_blur' --method_name='GD_swinir_2x' --dataset_name='set3c' --noise_level=0.01 --sigma_noise_max=0.01 --max_iter=60 --lambd=100 --eq=0 --results_folder='results_single_prior/'
python run_baselines.py --problem='SRx4' --method_name='GD_swinir_2x' --dataset_name='set3c' --noise_level=0.01 --sigma_noise_max=0.01 --max_iter=60 --lambd=50 --eq=0 --results_folder='results_single_prior/'

For SRx3:

python run_baselines.py --problem='gaussian_blur' --method_name='GD_swinir_2x' --dataset_name='set3c' --noise_level=0.01 --sigma_noise_max=0.01 --max_iter=60 --lambd=50 --eq=0 --results_folder='results_single_prior/'
python run_baselines.py --problem='motion_blur' --method_name='GD_swinir_2x' --dataset_name='set3c' --noise_level=0.01 --sigma_noise_max=0.01 --max_iter=60 --lambd=100 --eq=0 --results_folder='results_single_prior/'
python run_baselines.py --problem='SRx4' --method_name='GD_swinir_2x' --dataset_name='set3c' --noise_level=0.01 --sigma_noise_max=0.01 --max_iter=60 --lambd=50 --eq=0 --results_folder='results_single_prior/'

de-JPEG/denoising prior (click to expand)

srun python run_baselines.py --problem='gaussian_blur' --method_name='GD_scunet_jpeg' --dataset_name='set3c' --noise_level=0.01 --sigma_noise_min=0.0 --sigma_noise_max=0.1 --quality_min=40 --quality_max=80 --lambd=20 --max_iter=60 --results_folder='results_single_prior/'
srun python run_baselines.py --problem='motion_blur' --method_name='GD_scunet_jpeg' --dataset_name='set3c' --noise_level=0.01 --sigma_noise_min=0.0 --sigma_noise_max=0.01 --quality_min=40 --quality_max=80 --lambd=20 --max_iter=60 --results_folder='results_single_prior/'
srun python run_baselines.py --problem='SRx4' --method_name='GD_scunet_jpeg' --dataset_name='set3c' --noise_level=0.01 --sigma_noise_min=0.05 --sigma_noise_max=0.05 --quality_min=20 --quality_max=60 --lambd=50 --max_iter=80 --results_folder='results_single_prior/'

Inpainting prior (click to expand)

python run_baselines.py --problem='gaussian_blur' --method_name='GD_lama' --dataset_name='set3c' --p_mask_min=0.6 --p_mask_max=0.6 --sigma_noise_max=0.0 --lambd=50 --gamma=0.6 --max_iter=20 --equivariant=0 --results_folder='results_single_prior/'
python run_baselines.py --problem='motion_blur' --method_name='GD_lama' --dataset_name='set3c' --p_mask_min=0.6 --p_mask_max=0.6 --sigma_noise_max=0.0 --lambd=20 --gamma=0.6 --max_iter=20 --equivariant=0 --results_folder='results_single_prior/'
python run_baselines.py --problem='SRx4' --method_name='GD_lama' --dataset_name='set3c' --p_mask_min=0.6 --p_mask_max=0.6 --sigma_noise_max=0.0 --lambd=50 --gamma=0.8 --max_iter=20 --equivariant=0 --results_folder='results_single_prior/'

Combining priors

The above interpretation suggests that multiple restoration priors can be combined by simply averaging their outputs. To do so, we can use the --list_gamma_values argument to specify the $\gamma$ values for each prior. We observed that a good choice for combined priors is to use (a) the SCUNet de-JPEG prior, (b) the gaussian deblurring prior, and (c) the SR prior.

To run the combined prior experiments, you can use the following commands:

python run_baselines.py --problem='SRx4' --method_name='GD_multi_scunet_denoise_restormer_gaussian_swinir_3x' --dataset_name='set3c' --noise_level=0.01 --sigma_blur_min=0.01 --sigma_blur_max=0.1 --max_iter=30 --list_gamma_values 1.5 0.25 1.25 --motion_sigma_noise=0.005 --sigma_noise_min=0.0 --sigma_noise_max=0.1 --lambd=100 --results_folder='results_multiprior/' --equivariant=0

📝 Citation

If you find this work useful for your research, please cite our paper:

@inproceedings{terris2025fire,
  title={FiRe: Fixed-points of restoration priors for solving inverse problems},
  author={Terris, Matthieu and Kamilov, Ulugbek S and Moreau, Thomas},
  booktitle={Proceedings of the Computer Vision and Pattern Recognition Conference},
  pages={23185--23194},
  year={2025}
}