Macroeconomics

Quantum mechanics

Multiplier (economics)

Algorithm

Norm (philosophy)

Pure mathematics

Regularization (linguistics)

Rank (graph theory)

Total variation denoising

Astrophysics

Eigenvalues and eigenvectors

Economics

Computer science

Mathematical optimization

Variation (astronomy)

Tensor (intrinsic definition)

Physics

Pattern recognition (psychology)

Mathematics

Political science

Multispectral image

Artificial intelligence

Combinatorics

Noise reduction

Matrix norm

Imaging science

IEEE Journal of Selected Topics in Signal Processing

Some existing low-rank approximation approaches either need to predefine the rank values (such as the matrix/tensor factorization-based methods) or fail to consider local information of data (e.g., spatial or spectral smooth structure). To overcome these drawbacks, this paper proposes a new model called the tensor nuclear norm-based low-rank approximation with total variation regularization (TLR-TV) for color and multispectral image denoising. TLR-TV uses the tensor nuclear norm to encode the global low-rank prior of tensor data and the total variation regularization to preserve the spatial-spectral continuity in a unified framework. Including the hyper total variation (HTV) and spatial-spectral total variation (SSTV), we propose two TLR-TV-based algorithms, namely TLR-HTV and TLR-SSTV. Using the alternating direction method of multiplier, we further propose two simple algorithms to solve TLR-HTV and TLR-SSTV. Extensive experiments on simulated and real-world noisy images demonstrate that the proposed TLR-HTV and TLR-SSTV outperform the state-of-the-art methods in color and multispectral image denoising in terms of quantitative and qualitative evaluations.

Tensor Nuclear Norm-Based Low-Rank Approximation With Total Variation Regularization