Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

2006/11/16 by Michael Elad, Michal Aharon · 232 citations
Computer Science · Engineering · #Advanced Image Fusion Techniques #Image and Signal Denoising Methods #Sparse and Compressive Sensing Techniques

paper · doi:10.1109/tip.2006.881969

openalex publication_date 2006/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are considered: using the corrupted image itself, or training on a corpus of high-quality image database. Since the K-SVD is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm. This leads to a state-of-the-art denoising performance, equivalent and sometimes surpassing recently published leading alternative denoising methods.

Citations

• The design and use of steerable filters
• Atomic Decomposition by Basis Pursuit
• De-noising by soft-thresholding
• Ideal spatial adaptation by wavelet shrinkage

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Related

• Deep K-SVD Denoising
• Correlation Preserving Sparse Coding Over Multi-level Dictionaries for Image Denoising
• ℓ₁-K-SVD: A Robust Dictionary Learning Algorithm With Simultaneous Update
• Multiscale Sparsifying Transform Learning for Image Denoising
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