Combinatorics

Physics

Noise reduction

Mathematics

Matrix norm

Noise (video)

Algorithm

Image (mathematics)

Image restoration

Mathematical optimization

Impulse noise

Pixel

Rank (graph theory)

Mathematical analysis

Political science

Artificial intelligence

Norm (philosophy)

Eigenvalues and eigenvectors

Hankel matrix

Computer science

Quantum mechanics

Noise measurement

Gaussian noise

Low-rank approximation

Image processing

IEEE Transactions on Circuits and Systems for Video Technology

Exemplar-based image denoising algorithms have shown great potential for image restoration with a multitude of existing models. In this paper, we interpret nonlocal similar patch-based denoising as a problem of low-rank recovery. This offers a physically plausible model and unifies several existing techniques in a single low-rank recovery framework. The framework can handle complex noise models, such as zero-mean Gaussian noise, impulse noise, and any other noise that can be approximated by mixing these two kinds of noise. Moreover, we introduce a new nonconvex surrogate for the $l_{0}$ -norm and find the optimal solution of the optimization problems when the new norm is applied to low-rank recovery. The experimental results with different kinds of noise confirm the effectiveness of the proposed low-rank recovery framework and the new norm.

Exemplar-Based Denoising: A Unified Low-Rank Recovery Framework