MATLAB Code Implementation for Image Restoration: Fast Non-Local Means Filtering

This document explores an important approach in image restoration known as Non-Local Means filtering. Originally introduced by A. Buades and colleagues, this method has gained widespread adoption in the field of image processing. In Non-Local Means filtering, pixel color values are determined by calculating similarity measures with surrounding pixels. The algorithm computes weighted averages where similar patches contribute more significantly to the final value, effectively preserving image structures while reducing noise. However, the computational complexity of the standard implementation posed significant challenges for practical applications. To address this limitation, Buades et al. developed a fast implementation method called Fast Non-Local Means Filtering. This optimized approach leverages repetitive structures within images and employs strategic computational shortcuts, reducing the number of required operations to manageable levels. Key implementation techniques include patch precomputation, integral image utilization for rapid similarity calculations, and selective neighborhood searching. The MATLAB implementation typically involves several core functions: patch extraction using im2col or similar functions, efficient Euclidean distance calculations between patches, Gaussian weighting application based on similarity measures, and aggregation of weighted pixel values. The fast version often incorporates precomputed weights and optimized search windows to dramatically improve performance. Due to its balanced approach between computational efficiency and restoration quality, Fast Non-Local Means Filtering has become extensively applied in various image processing domains including image restoration, denoising, and super-resolution applications. It stands as an indispensable technique in modern image processing workflows, particularly valuable for handling noisy images while maintaining important texture details and structural information.