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Purpose To apply total generalized variation (TGV) and its combination with low‐rank and sparse decomposition (LRSD) (LTGV) to cerebral perfusion studies using low‐dose dynamic contrast‐enhanced (DCE) CT and to quantitatively evaluate their performances through comparisons with those without any regularizers and those of total variation (TV) and its combination with LRSD (LTV) using simulation and clinical data. Methods The simulation study used a realistic digital brain phantom. Low‐dose DCE‐CT images were reconstructed using the regularizers and primal‐dual algorithm. Subsequently, cerebral perfusion parameter (CPP) images were generated from them. Thereafter, their quality was evaluated based on the peak signal‐to‐noise ratio (PSNR) and structural similarity index measure (SSIM). Further, the accuracy of CPP estimation was evaluated through a linear regression analysis between the CPP values obtained by the above regularizers and those obtained from the noise‐free DCE‐CT images. In addition, the mean and standard deviation of the CPP were calculated (region analysis). In the clinical study, low‐dose DCE‐CT images were generated using normal‐dose images acquired from a patient, and CPP images were generated from them similar to that in the simulation study. Results When using LTV and LTGV, both PSNR and SSIM were higher than those of the other methods with increasing regularization parameter values. The results of the linear regression and region analyses demonstrated that TGV generally exhibited the best performance, followed by LTGV, and finally that of TV was significantly different from those of the other regularizers. Despite an overall consistency between the simulation and clinical results, certain inconsistencies appeared owing to the difference in generating low‐dose DCE‐CT images. Conclusions The results implied that TGV and LTGV were useful in improving the accuracy of CPP estimation using low‐dose DCE‐CT. This study provides an improved understanding of the performance of regularizers and is expected to aid in the selection of a suitable regularizer for low‐dose DCE‐CT perfusion studies.

Anomaly detection (AD) has emerged as a prominent area of research in hyperspectral imagery (HSI) processing. Traditional algorithms, such as low-rank and sparse matrix decomposition (LRaSMD), often struggle to effectively address challenges related to background interference, anomaly targets, and noise. To overcome these limitations, we propose a novel method that leverages both spatial and spectral features in HSI. Initially, the original HSI is segmented into several subspaces using the k-means method, which reduces redundancy among HSI bands. Subsequently, the fractional Fourier transform (FrFT) is applied within each subspace, enhancing the distinction between background and anomaly target information while simultaneously suppressing noise. To further improve the stability and discriminative power of the HSI, LRaSMD is employed. Finally, the modified Reed–Xiaoli (RX) detector is utilized to identify anomalies within each subspace. The results from these detections are then aggregated to produce a comprehensive final outcome. Experiments conducted on five real HSI data sets yield an average area under the curve (AUC) of 0.9761 with a standard deviation of 0.0156 for the proposed algorithm. These results indicate that our method is highly competitive in the field of anomaly detection.

Recovering the low-rank and sparse components from a given matrix is a challenging problem that has many real applications. This paper proposes a novel algorithm to address this problem by introducing a sparse prior on the low-rank component. Specifically, the low-rank component is assumed to be sparse in a transform domain and a sparse regularizer formulated as an ℓ 1 -norm term is employed to promote the sparsity. The truncated nuclear norm is used to model the low-rank prior, rather than the nuclear norm used in most existing methods, to achieve a better approximation to the rank of the considered matrix. Furthermore, an efficient solving method based on a two-stage iterative scheme is developed to address the raised optimization problem. The proposed algorithm is applied to deal with synthetic data and real applications including face image shadow removal and video background subtraction, and the experimental results validate the effectiveness and accuracy of the proposed approach as compared with other methods.

Ground-penetrating radar (GPR) is an effective geophysical electromagnetic method for underground target detection. However, the target response is usually overwhelmed by strong clutter, thus damaging the detection performance. To account for the nonparallel case of the antennas and the ground surface, a novel GPR clutter-removal method based on weighted nuclear norm minimization (WNNM) is proposed, which decomposes the B-scan image into a low-rank clutter matrix and a sparse target matrix by using a non-convex weighted nuclear norm and assigning different weights to different singular values. The WNNM method’s performance is evaluated using both numerical simulations and experiments with real GPR systems. Comparative analysis with the commonly used state-of-the-art clutter removal methods is also conducted in terms of the peak signal-to-noise ratio (PSNR) and the improvement factor (IF). The visualization and quantitative results demonstrate that the proposed method outperforms the others in the nonparallel case. Moreover, it is about five times faster than the RPCA, which is beneficial for practical applications.

Partial multi-label learning is of great significant interest due to accurate supervision is difficult to be obtained. Recently, multi-view learning has been developed to deal with partial multi-label learning tasks. Although few multi-view partial multi-label learning methods have been proposed, all of them are designed under the full-view assumption. However, due to the difficulties in multi-view data collection, some views may not contain complete information in real task. The appearance of missing views will affect the performance of traditional partial multi-label learning algorithms. To solve this problem, we propose a novel I ncomplete M ulti-V iew P artial M ulti-L abel learning (IMVPML) framework which makes use of incomplete multi-view feature representation and utilizes the low-rank and sparse decomposition scheme to remove the noisy labels. Specifically, we first learn a shared subspace across heterogenous incomplete views. Secondly, we utilize the low-rank and sparse decomposition scheme to obtain the ground-truth labels. Thirdly, we introduce a graph Laplacian regularization to constrain the ground-truth labels and impose orthogonality constraints on the correlations between subspace. Finally, a predictive model is learned by shared subspace and disambiguation labels. Enormous experimental results demonstrate that the proposed method can achieve competitive performance in solving the problem of incomplete multi-view partial multi-label learning.

As an unsupervised data representation neural network, auto-encoder (AE) has shown great potential in denoising, dimensionality reduction, and data reconstruction. Many AE-based background (BKG) modeling methods have been developed for hyperspectral anomaly detection (HAD). However, their performance is subject to their unbiased reconstruction of BKG and target pixels. This article presents a rather different low rank and sparse matrix decomposition (LRaSMD) method based on AE, named auto-encoder and independent target (AE-IT), for hyperspectral anomaly detection. First, the encoder weight matrix, obtained by a designed AE network, is utilized to construct a projector for generating a low-rank component in the encoder subspace. By adaptively and reasonably determining the number of neurons in the latent layer, the designed AE-based method can promote the reconstruction of BKG. Second, to ensure independence and representativeness, the component in the encoder orthogonal subspace is made into a sphere and followed by finding of unsupervised targets to construct an anomaly space. In order to mitigate the influence of noise on anomaly detection, sparse cardinality (SC) constraint is enforced on the component in the anomaly space for obtaining the sparse anomaly component. Finally, anomaly detector is constructed by combining Mahalanobi distance and multi-components, which include encoder component and sparse anomaly component, to detect anomalies. The experimental results demonstrate that AE-IT performs competitively compared to the LRaSMD-based models and AE-based approaches.

The problem of decomposing a given matrix into its low-rank and sparse components, known as robust principle component analysis (RPCA), has found many applications in variety of fields. In this problem, the goal is to recover the two components through constrained minimization of a combination of the rank function and l 0 norm. Oftentimes, exact recovery of the low-rank component is desired. Since the problem is NP-Hard, a convex relaxation where nuclear norm and l 1 norm are utilized to induce low-rank and sparsity is used. However, it may obtain suboptimal results since the nuclear norm cannot well approximate the rank function. This paper addresses the low-rank and sparse decomposition (LRSD) problem by utilizing a new nonconvex approximation function for the rank. In our LRSD approach, the nonconvex LL p norm is extended on singular values to obtain a new surrogate, called eLL p , for the rank function. To solve the associated minimization problem, an efficient algorithm based on alternating direction multiplier method (ADMM) and Majorization-Minimization (MM) algorithm is developed. To verify the effectiveness of the proposed method, it is applied to the synthetic data and real applications including face image shadow removal and image denoising. Experimental results show the effectiveness of the proposed method compared with the other methods in terms of the recovery errors and objective evaluations. In real applications of the images, our proposed method achieves higher recovery accuracy in a less time.

Video Synthetic Aperture Radar (SAR) has shown great potential in moving target detection and tracking. At present, most of the existing detection methods focus on the intensity information of the moving target shadow. According to the mechanism of shadow formation, some shadows of moving targets present low contrast, and their boundaries are blurred. Additionally, some objects with low reflectivity show similar features with them. These cause the performance of these methods to degrade. To solve this problem, this paper proposes a new moving target shadow detection method, which consists of background modeling and shadow detection based on intensity information and neighborhood similarity (BIIANS). Firstly, in order to improve the efficiency of image sequence generation, a fast method based on the Back-projection imaging algorithm (f-BP) is proposed. Secondly, due to the low-rank characteristics of stationary objects and the sparsity characteristics of moving target shadows presented in the image sequence, this paper introduces the low-rank sparse decomposition (LRSD) method to perform background modeling for obtaining better background (static objects) and foreground (moving targets) images. Because the shadows of moving targets appear in the same position in the original and the corresponding foreground images, the similarity between them is high and independent of their intensity. Therefore, using the BIIANS method can obtain better shadow detection results. Real W-band data are used to verify the proposed method. The experimental results reveal that the proposed method performs better than the classical methods in suppressing false alarms, missing alarms, and improving integrity.

Moving object detection which has attracted wide attention is the critical issue of computer vision. Consequently, the low-rank and sparse decomposition (LRSD) has been a powerful technology for extracting the moving object from videos which has achieved improvement for moving object detection. However, it still has some defaults such as the lower degree for approximating the low-rank and sparsity components, ignoring the spatial information of videos, being sensitive to noise, and so on. To address these problems mentioned above, we propose a new LRSD method which is named nonconvex norm and Laplacian scale mixture with salient map (NNLSMSM). It adopts the nonconvex γ -norm and the Laplacian scale mixture (LSM) to approximate the low-rank and sparsity components of traditional LRSD model for enhancing the degree of approximating. Meanwhile, a salient map mechanism which can effectively capture the spatial information from videos is introduced to NNLSMSM. In addition, we extend our proposed NNLSMSM method to a robust NNLSMSM (RNNLSMSM) method for enhancing its robustness via introducing a noise item. It can effectively solve the problem of being sensitive to noise. In addition, we adopt the alternating direction method of multipliers (ADMM) to solve our proposed NNLSMSM and RNNLSMSM methods. At last, extensive experiments which are performed on various popular datasets by some state-of-the-art methods demonstrate the effectiveness and superiority of our proposed NNLSMSM and RNNLSMSM methods.

Partial multi-label learning (PML) aims to learn from the training data where each training example is annotated with a candidate label set, among which only a subset is relevant. Despite the success of existing PML approaches, a major drawback of them lies in lacking of robustness to noisy side information. To tackle this problem, we introduce a novel partial multi-label learning with noisy side information approach, which simultaneously removes noisy outliers from the training instances and trains robust partial multi-label classifier for unlabeled instances prediction. Specifically, we first represent the observed sample set as a feature matrix and then decompose it into an ideal feature matrix and an outlier feature matrix by using the low-rank and sparse decomposition scheme, where the former is constrained to be low rank by considering that the noise-free feature information always lies in a low-dimensional subspace and the latter is assumed to be sparse by considering that the outliers are usually sparse among the observed feature matrix. Secondly, we refine an ideal label confidence matrix from the observed label matrix and use the graph Laplacian regularization to constrain the confidence matrix to keep the intrinsic structure among feature vectors. Thirdly, we constrain the feature mapping matrix to be low rank by utilizing the label correlations. Finally, we obtain both the ideal features and ground-truth labels via minimizing the loss function, where the augmented Lagrange multiplier algorithm and quadratic programming are incorporated to solve the optimization problem. Extensive experiments conducted on ten different data sets demonstrate the effectiveness of our proposed method.