# Orthogonal Constrained Minimization with Tensor ℓ2,p Regularization for HSI Denoising and Destriping

arXiv: https://arxiv.org/abs/2407.03605 · HTML: https://mlsanity.com/paper/2407.03605/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 63 references that are in the map.
- First posted on arXiv 4 Jul 2024.

## Builds on (most cited first, 10 of 10)

- [Quasi-Recurrent Neural Networks](https://mlsanity.com/paper/1611.01576/) (2016)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [Hyperspectral Image Denoising Employing a Spatial-Spectral Deep Residual Convolutional Neural Network](https://mlsanity.com/paper/1806.00183/) (2018)
- [3D Quasi-Recurrent Neural Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2003.04547/) (2020)
- [A globally convergent algorithm for nonconvex optimization based on block coordinate update](https://mlsanity.com/paper/1410.1386/) (2014)
- [Sparse PCA via l2,p-Norm Regularization for Unsupervised Feature Selection](https://mlsanity.com/paper/2012.14595/) (2020)
- [A two-stage method for spectral-spatial classification of hyperspectral images](https://mlsanity.com/paper/1806.00836/) (2018)
- [Multiplicative Noise Removal: Nonlocal Low-Rank Model and Its Proximal Alternating Reweighted Minimization Algorithm](https://mlsanity.com/paper/2002.07633/) (2020)
- [l2,p Matrix Norm and Its Application in Feature Selection](https://mlsanity.com/paper/1303.3987/) (2013)
- [Orthogonal Nonnegative Tucker Decomposition](https://mlsanity.com/paper/1910.09979/) (2019)

## Abstract (arXiv)

Hyperspectral images~(HSIs) are often contaminated by a mixture of noise such as Gaussian noise, dead lines, stripes, and so on. In this paper, we propose a multi-scale low-rank tensor regularized ℓ2,p (MLTL2p) approach for HSI denoising and destriping, which consists of an orthogonal constrained minimization model and an iterative algorithm with convergence guarantees. The model of the proposed MLTL2p approach is built based on a new sparsity-enhanced Multi-scale Low-rank Tensor regularization and a tensor ℓ2,p norm with (p∈ (0,1)). The multi-scale low-rank regularization for HSI denoising utilizes the global and local spectral correlation as well as the spatial nonlocal self-similarity priors of HSIs. The corresponding low-rank constraints are formulated based on independent higher-order singular value decomposition with sparsity enhancement on its core tensor to prompt more low-rankness. The tensor ℓ2,p norm for HSI destriping is extended from the matrix ℓ2,p norm. A proximal block coordinate descent algorithm is proposed in the MLTL2p approach to solve the resulting nonconvex nonsmooth minimization with orthogonal constraints. We show any accumulation point of the sequence generated by the proposed algorithm converges to a first-order stationary point, which is defined using three equalities of substationarity, symmetry, and feasibility for orthogonal constraints. In the numerical experiments, we compare the proposed method with state-of-the-art methods including a deep learning based method, and test the methods on both simulated and real HSI datasets. Our proposed MLTL2p method demonstrates outperformance in terms of metrics such as mean peak signal-to-noise ratio as well as visual quality.