Algorithm

Norm (philosophy)

Pure mathematics

Regularization (linguistics)

Rank (graph theory)

Total variation denoising

Computer science

Tensor (intrinsic definition)

Pattern recognition (psychology)

Mathematics

Political science

Hyperspectral imaging

Image denoising

Artificial intelligence

Geometry

Combinatorics

Noise reduction

IEEE Transactions on Geoscience and Remote Sensing

Hyperspectral images (HSIs) are normally corrupted by a mixture of various noise types, which degrades the quality of the acquired image and limits the subsequent application. In this article, we propose a novel denoising method for the HSI restoration task by combining nonlocal low-rank tensor decomposition and total variation regularization, which we refer to as TV-NLRTD. To simultaneously capture the nonlocal similarity and high spectral correlation, the HSI is first segmented into overlapping 3-D cubes that are grouped into several clusters by the k-means++ algorithm and exploited by low-rank tensor approximation. Spatial-spectral total variation (SSTV) regularization is then investigated to restore the clean HSI from the denoised overlapping cubes. Meanwhile, the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm facilitates the separation of the clean nonlocal low-rank tensor groups and the sparse noise. The proposed TV-NLRTD method is optimized by employing the efficient alternating direction method of multipliers (ADMM) algorithm. The experimental results obtained with both simulated and real hyperspectral data sets confirm the validity and superiority of the proposed method compared with the current state-of-the-art HSI denoising algorithms.

Hyperspectral Image Denoising With Total Variation Regularization and Nonlocal Low-Rank Tensor Decomposition