README.md

Lattice Boltzmann Method with stopping criterion for Image Denoising

This project presents a numerical experiment utilizing the five-speed lattice Boltzmann method (LBM D2Q5) to solve the Perona-Malik equation for denoising black-and-white images. The focus is on filtering Gaussian noise with zero mean and salt-and-pepper noise, assessing restoration quality through peak signal-to-noise ratio (PSNR). A decorrelation criterion for stopping the iterative algorithm is considered.

Key Features

• Noise Types: Handles both Gaussian and salt-and-pepper noise.
• Optimal Stopping Criterion: Implements a decorrelation criterion to determine the optimal stopping time for noise filtering, minimizing correlation between noise estimate and filtered signal.
• Performance Evaluation: Evaluate the LBM D2Q5 algorithm's efficiency using the BSD68 dataset.

The LBM_denoising.ipynb notebook provides a detailed overview of the experiment, including both visual and numerical analyses confirming the effectiveness of the LBM D2Q5 algorithm in improving PSNR and successfully filtering out noise from images.

References

1. P. Perona and J. Malik, «Scale-space and edge detection using anisotropic diffusion», 1990.
2. W. Zhang and B. Shi, «Application of Lattice Boltzmann Method to Image Filtering», 2012.
3. P. Mrazek and M. Navara, «Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering», 2003.