Low-Rank Optimization for Image Denoising via Sparse Dictionary Representations

Resource Overview

Denoise images by applying sparse coding to local patches using pre-trained overcomplete dictionaries, followed by patch aggregation through averaging. This technique employs sparse and redundant representations over learned dictionaries, as detailed in "Image Denoising Via Sparse and Redundant Representations over Learned Dictionaries." The algorithm involves dictionary initialization, patch extraction, L1-norm optimization for sparse coding (e.g., via Orthogonal Matching Pursuit), and weighted averaging to reconstruct the denoised image.

Detailed Documentation

This method performs image denoising by sparsely representing each image patch using a pre-trained overcomplete dictionary and aggregating the reconstructed patches through averaging. Detailed documentation can be found in the paper "Image Denoising Via Sparse and Redundant Representations over Learned Dictionaries." Implementation typically involves: 1. Dictionary training using K-SVD or online dictionary learning algorithms 2. Patch extraction with sliding window approach (e.g., 8×8 pixel blocks) 3. Sparse coding via optimization methods like OMP (Orthogonal Matching Pursuit) to solve min||x||₁ subject to ||Dx - y||₂ ≤ ε 4. Patch reconstruction using x̂ = Dx where D is the learned dictionary 5. Aggregation through overlapping patch averaging with Hanning window weighting The algorithm reduces noise while preserving image structures by leveraging the sparsity-promoting properties of overcomplete dictionaries. Key parameters include patch size, dictionary atoms count, and sparsity constraint λ in the L1-regularized optimization problem min||Dx - y||₂² + λ||x||₁.