A Robust Tensor-Based Submodule Clustering for Imaging Data Using l12 Regularization and Simultaneous Noise Recovery via Sparse and Low Rank Decomposition Approach

The massive generation of data, which includes images and videos, has made data management, analysis, information extraction difficult in recent years. To gather relevant information, this large amount of data needs to be grouped. Real-life data may be noise corrupted during data collection or transmission, and the majority of them are unlabeled, allowing for the use of robust unsupervised clustering techniques. Traditional clustering techniques, which vectorize the images, are unable to keep the geometrical structure of the images. Hence, a robust tensor-based submodule clustering method based on l12 regularization with improved clustering capability is formulated. The l12 induced tensor nuclear norm (TNN), integrated into the proposed method, offers better low rankness while retaining the self-expressiveness property of submodules. Unlike existing methods, the proposed method employs a simultaneous noise removal technique by twisting the lateral image slices of the input data tensor into frontal slices and eliminates the noise content in each image, using the principles of the sparse and low rank decomposition technique. Experiments are carried out over three datasets with varying amounts of sparse, Gaussian and salt and pepper noise. The experimental results demonstrate the superior performance of the proposed method over the existing state-of-the-art methods.

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Hyperspectral Anomaly Detection with Harmonic Analysis and Low-Rank Decomposition

Remote Sensing ◽

10.3390/rs11243028 ◽

2019 ◽

Vol 11 (24) ◽

pp. 3028 ◽

Cited By ~ 1

Author(s):

Pei Xiang ◽

Jiangluqi Song ◽

Huan Li ◽

Lin Gu ◽

Huixin Zhou

Keyword(s):

Anomaly Detection ◽

Harmonic Analysis ◽

Hyperspectral Image ◽

Low Rank ◽

Superior Performance ◽

Alternative Methods ◽

Qualitative Assessment ◽

Redundant Information ◽

Rank Decomposition ◽

Low Rank Decomposition

Hyperspectral anomaly detection methods are often limited by the effects of redundant information and isolated noise. Here, a novel hyperspectral anomaly detection method based on harmonic analysis (HA) and low rank decomposition is proposed. This paper introduces three main innovations: first and foremost, in order to extract low-order harmonic images, a single-pixel-related HA was introduced to reduce dimension and remove redundant information in the original hyperspectral image (HSI). Additionally, adopting the guided filtering (GF) and differential operation, a novel background dictionary construction method was proposed to acquire the initial smoothed images suppressing some isolated noise, while simultaneously constructing a discriminative background dictionary. Last but not least, the original HSI was replaced by the initial smoothed images for a low-rank decomposition via the background dictionary. This operation took advantage of the low-rank attribute of background and the sparse attribute of anomaly. We could finally get the anomaly objectives through the sparse matrix calculated from the low-rank decomposition. The experiments compared the detection performance of the proposed method and seven state-of-the-art methods in a synthetic HSI and two real-world HSIs. Besides qualitative assessment, we also plotted the receiver operating characteristic (ROC) curve of each method and report the respective area under the curve (AUC) for quantitative comparison. Compared with the alternative methods, the experimental results illustrated the superior performance and satisfactory results of the proposed method in terms of visual characteristics, ROC curves and AUC values.

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Suppressing the Spikes in Electroencephalogram via an Iterative Joint Singular Spectrum Analysis and Low-Rank Decomposition Approach

Sensors ◽

10.3390/s20020341 ◽

2020 ◽

Vol 20 (2) ◽

pp. 341 ◽

Cited By ~ 2

Author(s):

Zikang Tian ◽

Bingo Wing-Kuen Ling ◽

Xueling Zhou ◽

Ringo Wai-Kit Lam ◽

Kok-Lay Teo

Keyword(s):

Spectrum Analysis ◽

Singular Spectrum Analysis ◽

Threshold Value ◽

Low Rank ◽

Wave Band ◽

Decomposition Approach ◽

Singular Spectrum ◽

Unit Energy ◽

Rank Decomposition ◽

Low Rank Decomposition

The novelty and the contribution of this paper consists of applying an iterative joint singular spectrum analysis and low-rank decomposition approach for suppressing the spikes in an electroencephalogram. First, an electroencephalogram is filtered by an ideal lowpass filter via removing its discrete Fourier transform coefficients outside the δ wave band, the θ wave band, the α wave band, the β wave band and the γ wave band. Second, the singular spectrum analysis is performed on the filtered electroencephalogram to obtain the singular spectrum analysis components. The singular spectrum analysis components are sorted according to the magnitudes of their corresponding eigenvalues. The singular spectrum analysis components are sequentially added together starting from the last singular spectrum analysis component. If the variance of the summed singular spectrum analysis component under the unit energy normalization is larger than a threshold value, then the summation is terminated. The summed singular spectrum analysis component forms the first scale of the electroencephalogram. The rest singular spectrum analysis components are also summed up together separately to form the residue of the electroencephalogram. Next, the low-rank decomposition is performed on the residue of the electroencephalogram to obtain both the low-rank component and the sparse component. The low-rank component is added to the previous scale of the electroencephalogram to obtain the next scale of the electroencephalogram. Finally, the above procedures are repeated on the sparse component until the variance of the current scale of the electroencephalogram under the unit energy normalization is larger than another threshold value. The computer numerical simulation results show that the spike suppression performance based on our proposed method outperforms that based on the state-of-the-art methods.

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Joint reconstruction and low-rank decomposition for dynamic inverse problems

Inverse Problems and Imaging ◽

10.3934/ipi.2021059 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Simon Arridge ◽

Pascal Fernsel ◽

Andreas Hauptmann

Keyword(s):

Inverse Problems ◽

Measurement Data ◽

Nonnegative Matrix ◽

Low Rank ◽

Decomposition Approach ◽

Temporal Behaviour ◽

Joint Reconstruction ◽

Rank Decomposition ◽

Dynamic Inverse ◽

Low Rank Decomposition

<p style='text-indent:20px;'>A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work, we consider the case, where the target can be represented by a decomposition of spatial and temporal basis functions and hence can be efficiently represented by a low-rank decomposition. We then propose a joint reconstruction and low-rank decomposition method based on the Nonnegative Matrix Factorisation to obtain the unknown from highly undersampled dynamic measurement data. The proposed framework allows for flexible incorporation of separate regularisers for spatial and temporal features. For the special case of a stationary operator, we can effectively use the decomposition to reduce the computational complexity and obtain a substantial speed-up. The proposed methods are evaluated for three simulated phantoms and we compare the obtained results to a separate low-rank reconstruction and subsequent decomposition approach based on the widely used principal component analysis.</p>

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