Subspace Low-rank Representation Research Articles

Discriminant Subspace Low-Rank Representation Algorithm for Electroencephalography-Based Alzheimer's Disease Recognition.

Alzheimer’s disease (AD) is a chronic progressive neurodegenerative disease that often occurs in the elderly. Electroencephalography (EEG) signals have a strong correlation with neuropsychological test results and brain structural changes. It has become an effective aid in the early diagnosis of AD by exploiting abnormal brain activity. Because the original EEG has the characteristics of weak amplitude, strong background noise and randomness, the research on intelligent AD recognition based on machine learning is still in the exploratory stage. This paper proposes the discriminant subspace low-rank representation (DSLRR) algorithm for EEG-based AD and mild cognitive impairment (MCI) recognition. The subspace learning and low-rank representation are flexibly integrated into a feature representation model. On the one hand, based on the low-rank representation, the graph discriminant embedding is introduced to constrain the representation coefficients, so that the robust representation coefficients can preserve the local manifold structure of the EEG data. On the other hand, the least squares regression, principle component analysis, and global graph embedding are introduced into the subspace learning, to make the model more discriminative. The objective function of DSLRR is solved by the inexact augmented Lagrange multiplier method. The experimental results show that the DSLRR algorithm has good classification performance, which is helpful for in-depth research on AD and MCI recognition.

Hyperspectral image restoration by subspace representation with low‐rank constraint and spatial‐spectral total variation

Hyperspectral images (HSIs) restoration is an important preprocessing step. The spectral vectors in HSI can be separated into different classification based on the land-covers, which means the spectral space can be regarded as the union of several low-rank subspaces. Subspace low-rank representation (SLRR) is powerful in exploring the inner low-rank structure and has been applied for HSI restoration. However, the traditional SLRR only seek for the rank-minimum representation under a given dictionary, which may treat the structured sparse noise as inherent low-rank components. In addition, the SLRR framework cannot make full use of the spatial information. In this study, a framework named subspace representation with low-rank constraint and spatial-spectral total variation is proposed for HSI restoration. In which, an artificial rank constraint is introduced to control the rank of the representation result, which can improve the removal of the structured sparse noise and exploit the intrinsic structure of spectral space more effectively. Meanwhile, the spatial-spectral total variation regularisation is applied to enhance the spatial and spectral smoothness. Several experiments conducted in simulated and real HSI datasets demonstrate that the proposed method can achieve a state-of-the-art performance both in visual quality and quantitative assessments.

Hyperspectral Image Denoising via Subspace Low-rank Representation and Spatial–spectral Total Variation

Abstract Hyperspectral images (HSIs) acquired actually often contain various types of noise, such as Gaussian noise, impulse noise, and dead lines. On the basis of land covers, the spectral vectors in HSI can be separated into different classifications, which means the spectral space can be regarded as a union of several low-rank (LR) subspaces rather than a single LR subspace. Recently, LR constraint has been widely applied for denoising HSI. However, those LR-based methods do not constrain the intrinsic structure of spectral space. And these methods cannot make better use of the spatial or spectral features in an HSI cube. In this article, a framework named subspace low-rank representation combined with spatial‐spectral total variation regularization (SLRR-SSTV) is proposed for HSI denoising, where the SLRR is introduced to more precisely satisfy the low-rank property of spectral space, and the SSTV regularization is involved for the spatial and spectral smoothness enhancement. An inexact augmented Lagrange multiplier method by alternative iteration is employed for the SLRR-SSTV model solution. Both simulated and real HSI experiment results demonstrate that the proposed method can achieve a state-of-the-art performance in HSI denoising.

Fast Superpixel Based Subspace Low Rank Learning Method for Hyperspectral Denoising

Sequential data, such as video frames and event data, have been widely applied in the real-world. As a special kind of sequential data, hyperspectral images (HSIs) can be regarded as a sequence of 2-D images in the spectral dimension, which can be effectively utilized for distinguishing different land-covers according to the spectral sequences. This paper presents a novel noise reduction method based on superpixel-based subspace low rank representation for hyperspectral imagery. First, under the framework of a linear mixture model, the original hyperspectral cube is assumed to be low rank in the spectral domain, which could be represented by decomposing HSI data into two sub-matrices of lower ranks. Meanwhile, due to the high correlation of neighboring pixels, the spectra within each neighborhood would also promote low rankness, and the local spatial low rankness could be exploited by enforcing the nuclear norm within superpixel-based regions in the decomposed subspace. The superpixels are easily and effectively generated by utilizing state-of-the-art superpixel segmentation algorithms in the first principal component of the original HSI. Moreover, benefiting from the subspace decomposition, the proposed method has an overwhelming superiority in computational cost than the state-of-the-art LR-based methods. The final model could be efficiently solved by the augmented Lagrangian method. Experimental results on simulated and real hyperspectral data sets validate that the proposed method produces superior performance than other state-of-the-art denoising methods in terms of quantitative assessment and visual quality.