Algorithm

Norm (philosophy)

Ecology

Pure mathematics

Biology

Astrophysics

Computer science

Decomposition

Variation (astronomy)

Geology

Image resolution

Tensor (intrinsic definition)

Physics

Organic chemistry

Pattern recognition (psychology)

Mathematics

Image (mathematics)

Political science

Multispectral image

Hyperspectral imaging

Tensor decomposition

Smoothness

Tucker decomposition

Mathematical analysis

Artificial intelligence

Geometry

Remote sensing

Chemistry

Superresolution

Piecewise

Computer vision

IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing

The hyperspectral image superresolution (HSI-SR) problem aims to improve the spatial quality of a low spatial resolution HSI by fusing the LR-HSI with the corresponding high spatial resolution multispectral image. The generated HSI with high spatial quality, i.e., the target high spatial resolution hyperspectral image (HR-HSI), generally has some fundamental latent properties, e.g., the sparsity, and the piecewise smoothness along with the three modes (i.e., width, height, and spectral mode). However, limited works consider both properties in the HSI-SR problem. In this work, a novel unidirectional total variation (TV) based approach is been proposed. On the one hand, we consider that the target HR-HSI exhibits both the sparsity and the piecewise smoothness on the three modes, and they can be depicted well by the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm and TV, respectively. On the other hand, we utilize the classical Tucker decomposition to decompose the target HR-HSI (a three-mode tensor) as a sparse core tensor multiplied by the dictionary matrices along with the three modes. Especially, we impose the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm on core tensor to characterize the sparsity and the unidirectional TV on three dictionaries to characterize the piecewise smoothness. The proximal alternating optimization scheme and the alternating direction method of multipliers are used to iteratively solve the proposed model. Experiments on three common datasets illustrate that the proposed approach has better performance than some current state-of-the-art HSI-SR methods. Please find source code from: https://liangjiandeng.github.io/.

Hyperspectral Image Superresolution Using Unidirectional Total Variation With Tucker Decomposition