Dictionary Atoms Research Articles

Dual Collaborative Constraints Regularized Low-Rank and Sparse Representation via Robust Dictionaries Construction for Hyperspectral Anomaly Detection

The low rank and sparse representation (LRSR) technique has attracted increasing attention for hyperspectral anomaly detection (HAD). Although a large quantity of research based on LRSR for HAD is proposed, the detection performance is still limited, due to the unsatisfactory dictionary construction and insufficient consideration of global and local characteristics. To tackle the above-mentioned concern, a novel HAD method, termed dual collaborative constraints regularized low-rank and sparse representation via robust dictionaries construction, is proposed in this article. Concretely, a robust dictionary construction strategy, which thoroughly excavates the potential of the density estimation model and local outlier factor, is proposed to yield pure and representative dictionary atoms. To fully exploit the global and local characteristics of hyperspectral images, dual collaborative constraints corresponding to the background and anomaly components are imposed on the LRSR model. Notably, two weighted matrices are further exerted on the representation coefficients to improve the effect of collaborative constraints, considering the fact that the surrounding pixels similar to the testing pixel should be given a large weight, otherwise the weight is expected to be small. In this way, the background and anomaly components can be well modeled. Additionally, a nonlinear transformation operation, which combines the output of the density estimation model and local outlier factor with the detection result derived from the LRSR model, is developed to suppress the background. The experiments conducted on one simulated dataset and three real datasets demonstrate the superiority of the proposed method compared with the four typical methods and four state-of-the-art methods.

Matrix Factorization With Framelet and Saliency Priors for Hyperspectral Anomaly Detection

Hyperspectral anomaly detection aims to separate sparse anomalies from low-rank background components. A variety of detectors have been proposed to identify anomalies, but most of them tend to emphasize characterizing backgrounds with multiple types of prior knowledge and limited information on anomaly components. To tackle these issues, this paper simultaneously focuses on two components and proposes a matrix factorization method with framelet and saliency priors to handle the anomaly detection problem. We first employ a framelet to characterize nonnegative background representation coefficients, as they can jointly maintain sparsity and piecewise smoothness after framelet decomposition. We then exploit saliency prior knowledge to measure each pixel’s potential to be an anomaly. Finally, we incorporate the pure pixel index with Reed-Xiaoli’s method to possess representative dictionary atoms. We solve the optimization problem by using a block successive upper-bound minimization framework with guaranteed convergence. Experiments conducted on benchmark hyperspectral datasets demonstrate that the proposed method outperforms some state-of-the-art anomaly detection methods.

High-Dimensional Generalized Orthogonal Matching Pursuit With Singular Value Decomposition

Matching pursuit (MP) is an algorithm which can reconstruct signal accurately, and is widely used in signal processing. However, MP algorithm has efficiency problem in processing large amount of data like five-dimensional (5D) seismic data. Generalized orthogonal matching pursuit with singular value decomposition (SVD_GOMP) is an algorithm which can improve the calculation efficiency a lot, and keeps the advantage of high accuracy. In this study, a redundant atom dictionary includes incident angles and azimuth is built. Then the five-dimensional seismic data is reconstructed efficiently and accurately by the generalize orthogonal matching pursuit with singular value decomposition algorithm. Compared with traditional matching pursuit method, the proposed method decomposes the five-dimensional seismic data at the same time and recovers the angle information efficiently. The reconstructed results of synthetic and field data examples are utilized to demonstrate the feasibility, computational efficiency and precision of the proposed method.

Using dictionary learning for clutter reduction in GPR B-scan images

ABSTRACT Ground-penetrating radar (GPR) has been widely used to detect subsurface objects. However, the target reflection experiences interference owing to clutter, such as direct coupling, interface reflection, and other undesired reflections. Reducing such clutter is a valuable processing step to improve detection accuracy. This letter proposes a GPR clutter reduction algorithm based on dictionary learning (DL). DL learns an adaptive dictionary that can sparsely represent the GPR B-scan image and enable clutter suppression. The learned dictionary atoms are divided into target atoms and clutter atoms, the target component and the clutter component can be reconstructed using these two types of dictionary atoms, respectively. The performance of the proposed algorithm is validated using both simulation data and real GPR data. The results of the visual evaluation and quantitative analysis demonstrate that the proposed algorithm outperforms the existing clutter reduction algorithms.

Identification of Time-Varying External Force Using Group Sparse Regularization and Redundant Dictionary.

How to accurately identify unknown time-varying external force from measured structural responses is an important engineering problem, which is critical for assessing the safety condition of the structure. In the context of a few available accelerometers, this paper proposes a novel time-varying external force identification method using group sparse regularization based on the prior knowledge in the redundant dictionary. Firstly, the relationship between time-varying external force and acceleration responses is established, and a redundant dictionary is designed to create a sparse expression of external force. Then, the relevance of atoms in the redundant dictionary is revealed, and this prior knowledge is used to determine the group structures of atoms. As a result, a force identification governing equation is formulated, and the group sparse regularization is reasonably introduced to ensure the accuracy of the identified results. The contribution of this paper is that the group structures of atoms are reasonably determined based on prior knowledge, and the complexity in the process for identifying external force from measured acceleration responses is reduced. Finally, the effectiveness of the proposed method is demonstrated by numerical simulations and an experimental structure. The illustrated results show that, compared with the force identification method based on the standard l1-norm regularization, the proposed method can further improve the identified accuracy of unknown external force and greatly enhance the computational efficiency for the force identification problem.

Towards the characterization of the tumor microenvironment through dictionary learning-based interpretable classification of multiplexed immunofluorescence images

Objective. Histology image analysis is a crucial diagnostic step in staging and treatment planning, especially for cancerous lesions. With the increasing adoption of computational methods for image analysis, significant strides are being made to improve the performance metrics of image segmentation and classification frameworks. However, many developed frameworks effectively function as black boxes, granting minimal context to the decision-making process. Thus, there is a need to develop methods that offer reasonable discriminatory power and a biologically-informed intuition to the decision-making process. Approach. In this study, we utilized and modified a discriminative feature-based dictionary learning (DFDL) paradigm to generate a classification framework that allows for discrimination between two distinct clinical histologies. This framework allows us (i) to discriminate between 2 clinically distinct diseases or histologies and (ii) provides interpretable group-specific representative dictionary image patches, or ‘atoms’, generated during classifier training. This implementation is performed on multiplexed immunofluorescence images from two separate patient cohorts- a pancreatic cohort consisting of cancerous and non-cancerous tissues and a metastatic non-small cell lung cancer (mNSCLC) cohort of responders and non-responders to an immunotherapeutic treatment regimen. The analysis was done at both the image-level and subject-level. Five cell types were selected, namely, epithelial cells, cytotoxic lymphocytes, antigen presenting cells, HelperT cells, and T-regulatory cells, as our phenotypes of interest. Results. We showed that DFDL had significant discriminant capabilities for both the pancreatic pathologies cohort (subject-level AUC-0.8878) and the mNSCLC immunotherapy response cohort (subject-level AUC-0.7221). The secondary analysis also showed that more than 50% of the obtained dictionary atoms from the classifier contained biologically relevant information. Significance. Our method shows that the generated dictionary features can help distinguish patients presenting two different histologies with strong sensitivity and specificity metrics. These features allow for an additional layer of model interpretability, a highly desirable element in clinical applications for identifying novel biological phenomena.

MADPL-net: Multi-layer attention dictionary pair learning network for image classification

With the great success of deep neural networks, combining deep learning with traditional dictionary learning has become a hot issue. However, the performance of these methods is still limited for several reasons. First, some existing methods update dictionary learning and classifier as two independent modules, which limits the classification performance. Second, the non-attention dictionary is learned to represent all images, reducing the model representation flexibility. In this paper, we design a novel end-to-end model named Multi-layer Attention Dictionary Pair Learning Network (MADPL-net), which integrates the learning schemes of the convolutional neural network, deep encoder learning, and attention dictionary pair learning (ADicL) into a unified framework. The encoder layer contains the ADicL block, which selects more image-attentive atoms in the dictionary pair block via the softmax function to ensure MADPL-net classification capability. In addition, ADicL schema can yield discriminative dictionary atoms and feature maps with high inter-class separation and high intra-class compactness. To improve the sparse representation learning performance, MADPL-net adds l1−norm constraint of the analysis dictionary to the cross-entropy loss function. Extensive experiments show that MADPL-net can achieve excellent performance over other state-of-the-arts.

A Bayesian Approach for Joint Discriminative Dictionary and Classifier Learning

Sparse representation has been widely applied to image classification, where the key issue is to extract a suitable discriminative dictionary. To this end, we propose a joint dictionary and classifier learning algorithm based on a parameterized Bayesian model. Therein, the Gaussian priors of a dictionary endow it with the capability of discrimination and representation. Moreover, we introduce a multivariate Gaussian prior for the sparse codes to achieve group sparsity, thereby substantially improving the classification performance. Furthermore, the sparse codes are estimated by a group-sparse Bayesian learning (GSBL) method, and the dictionary atoms are updated sequentially by maximizing a posterior. Moreover, to avoid manual parameter adjustment, the hyperparameters are optimized by an evidence maximization method. Accordingly, we develop a classification scheme via GSBL. Finally, extensive experiments are conducted on six benchmark datasets of face classification, object recognition, handwritten recognition, and scene categorization to substantiate the effectiveness and superiority of the proposed method.

OBJECT DETECTION BASED ON SPECTRAL ANALYSIS USING SOBEL AND ROBERTS EDGE DETECTION ALGORITHM

Aim: This paper proposes novel object detection (OD) approach based on a thorough examination of the image's details and its approximate density chart. Results: Our proposed OD approach is divided into two phases. Knowledge about Spatial Distribution of Objects obtained from a density map that is used to compute initial object positions. With the aid of the original object positions estimated, a saliency map that provides entity boundaries is then used to calculate the bounding boxes with precision, which is inspired by human attention to detail. The scale variance of objects induced by uncertain perspective is a common problem in object density map estimation. A new method for estimating the prior focus for map for any image is proposed. Sobel and Roberts Edge Detection Algorithm are used in this study. The proposed approach is based on sparse defocus dictionary learning on a newly constructed dataset. The focus power is determined by the number of non-zero coefficients of the dictionary atoms. Conclusion: The algorithm's output can capture spatial features and pick the threshold type in a variety of ways. HIGHLIGHTS: Object detection based on spectral analysis using Sobel and Roberts edge detection algorithm proved to be effective when compared with existing methodologies.

Non-negative constrained dictionary learning for compressed sensing of ECG signals

Objective. Overcomplete dictionaries are widely used in compressed sensing (CS) to improve the quality of signal reconstruction. However, dictionary learning under the -norm or -norm constraint inevitably produces dictionary atoms that are negatively correlated with the original signal; meanwhile, when we use a sparse linear combination of dictionary atoms to represent a signal, it is suboptimal for the dictionary atoms to “cancel each other out” by addition and subtraction to approximate the sample. In this paper, we propose a non-negative constrained dictionary learning (NCDL) algorithm to improve the reconstruction performance of CS with electrocardiogram (ECG) signals. Approach. Non-NCDL was divided into an encoding stage and a dictionary learning stage. In the encoding stage, non-negative constraints were imposed on the encoding coefficients and obtained the sparse solution using the alternating direction method of multipliers. At the same time, a penalty term was integrated into the objective function in order to remove small coding coefficients and achieve the effect of sparse coding. In the dictionary learning stage, the block coordinate descent algorithm was utilized to update the dictionary with a view to obtaining an overcomplete dictionary. Results. The performance of the proposed NCDL algorithm was evaluated using the standard MIT-BIH database. Quantitative performance metrics, such as percent root mean square difference (PRD1) and root mean square error, were compared with existing CS approaches to quantify the efficacy of the proposed scheme. For a PRD1 value of 9%, the compression ratio (CR) of the NCDL approach was around 2.78. When CR ranged from 1.05 to 2.78, the proposed NCDL approach outperformed the method of optimal direction, k-means singular value decomposition, and online dictionary learning approaches in ECG signal reconstruction based on CS. Significance. This promising preliminary result demonstrates the capability and feasibility of the proposed bioimpedance method and may open up a new direction for this application. The non-NCDL method proposed in this paper can be used to obtain a sparse basis and improve the performance of CS reconstruction.

Retrieving useful signals from highly corrupted erratic noise using robust residual dictionary learning

Seismic denoising will inevitably cause signal leakage, which is seen as coherent signal energy in the removed noise profile. Most traditional methods either ignore the signal leakage while maintaining clean denoised data or adjust parameters to decrease the signal leakage while causing more residual noise in the denoised data. The local signal-and-noise orthogonalization method can help retrieve the leaked signals without bringing significant residual noise. However, when seismic data contain erratic noise, the local orthogonalization method does not work properly because of the unstable inversion when solving the local orthogonalization weight due to the large-amplitude erratic noise. We propose a robust dictionary learning and sparse coding algorithm to retrieve the leaked signals. In this robust method, we substitute the L2-norm regularized sparse coding model with a Huber-norm sparse coding model, which is solved iteratively via a robust algorithm. The dictionary atoms used to retrieve the leaked signals are first learned from the initial estimate of signals and then updated during the robust iterations. Synthetic and field data examples containing erratic noise are used to demonstrate the effectiveness of the proposed method.

Dictionary Learning-Cooperated Matrix Decomposition for Hyperspectral Target Detection

Hyperspectral target detection is one of the most challenging tasks in remote sensing due to limited spectral information. Many algorithms based on matrix decomposition (MD) are proposed to promote the separation of the background and targets, but they suffer from two problems: (1) Targets are detected with the criterion of reconstruction residuals, and the imbalanced number of background and target atoms in union dictionary may lead to misclassification of targets. (2) The detection results are susceptible to the quality of the apriori target spectra, thus obtaining inferior performance because of the inevitable spectral variability. In this paper, we propose a matrix decomposition-based detector named dictionary learning-cooperated matrix decomposition (DLcMD) for hyperspectral target detection. The procedure of DLcMD is two-fold. First, the low rank and sparse matrix decomposition (LRaSMD) is exploited to separate targets from the background due to its insensitivity to the imbalanced number of background and target atoms, which can reduce the misclassification of targets. Inspired by dictionary learning, the target atoms are updated during LRaSMD to alleviate the impact of spectral variability. After that, a binary hypothesis model specifically designed for LRaSMD is proposed, and a generalized likelihood ratio test (GLRT) is performed to obtain the final detection result. Experimental results on five datasets have shown the reliability of the proposed method. Especially in the Los Angeles-II dataset, the area under the curve (AUC) value is nearly 16% higher than the average value of the other seven detectors, which reveals the superiority of DLcMD in hyperspectral target detection.

An improved compressed sensing method for dynamic impact signals based on cubic spline interpolation.

During the dynamic acquisition of impact signals, a high sampling frequency brings significant challenges to the analog-to-digital converter and other test systems. To address this issue, in this study, an improved compressed sensing (CS) method is proposed for the measurement of impact signals based on cubic spline interpolation (CSI). According to the characteristics of the dynamic impact signal, a random non-uniform sampling strategy combining CS and CSI is presented. The CSI obviously reduces the number of observation points required by the traditional CS. To resolve the problem that the traditional orthogonal matching pursuit (OMP) algorithm can only guarantee the local optimal solution but cannot obtain the global optimal solution, an improved orthogonal matching pursuit (IOMP) algorithm is proposed. First, n atoms related to residuals are selected to build a local atomic dictionary. Subsequently, the atom most relevant to the signal observation result is selected from the local atomic dictionary. The iteration process is repeated until enough atoms are selected. The IOMP algorithm effectively improves the success rate of reconstruction. Finally, an impact signals test platform based on the Machete hammer is established. The results of theoretical simulations and several experiments indicate that the data reconstruction error of the proposed improved CS method for impact signals is approximately 5.0%.

A Gaussian High-Dimensional Random Matrix-Based Method for Detecting Abnormal Student Behaviour in Chinese Language Classrooms

In this paper, a Gaussian high-dimensional random matrix approach is used to conduct an in-depth study and analysis of the detection of abnormal student behaviour in Chinese language classrooms, and a corresponding model is designed for practical application. The Gaussian high-dimensional random matrix technique and recurrent neural network technique are applied to build a basic technical framework for intelligent proctoring. An innovative method of human posture estimation is used to complete the proctoring task, and the structure of the Gaussian high-dimensional random matrix method is simplified and the model is compressed to achieve real-time and parallelism of the method. A PolSAR sparse representation classification (OGRM_SRC) algorithm based on orthogonal Gaussian random matrices (OGRM) is proposed to construct an observation dictionary based on polarisation features and OGRM to select typical ground target samples in polarized feature images. The system not only functions as a psychometric assessment of students but also is capable of detecting and analysing abnormal student behaviour based on the improved forest algorithm. The residuals of the pixel to be classified are calculated relative to each atom in the observation dictionary, and the minimum reconstruction residual is used as the classification criterion. The OGRM_SRC algorithm is applied to classify the pixel, and the final classification results are obtained and evaluated for accuracy. We propose a fine-grained action recognition optimisation method for recurrent neural networks, fusing temporal attention information and spatial attention information to improve the action recognition method and improve the model’s ability to recognise fine-grained abnormal behaviours such as looking left, looking right, and copying with head down. Based on this, we conducted some comparative experiments to validate the effectiveness of our work and verified that the system achieved a recognition efficiency of 76.8 FPS and a recognition accuracy of 98.5% in a graphical computing processor.

Sampling Rates for $$\ell ^1$$-Synthesis

This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the \(\ell ^1\)-synthesis basis pursuit allows for a simultaneous estimation of a coefficient representation as well as the sought-for signal. However, due to linear dependencies within redundant dictionary atoms, it might be impossible to identify a specific representation vector, although the actual signal is still successfully recovered. The present manuscript studies both estimation problems from a non-uniform, signal-dependent perspective. By utilizing recent results on the convex geometry of linear inverse problems, the sampling rates describing the phase transitions of each formulation are identified. In both cases, they are given by the conic Gaussian mean width of an \(\ell ^1\)-descent cone that is linearly transformed by the dictionary. In general, this expression does not allow for a simple calculation by following the polarity-based approach commonly found in the literature. Hence, two upper bounds involving the sparsity structure of coefficient representations are provided: The first one is based on a local condition number and the second one on a geometric analysis that makes use of the thinness of high-dimensional polyhedral cones with not too many generators. It is furthermore revealed that both recovery problems can differ dramatically with respect to robustness to measurement noise—a fact that seems to have gone unnoticed in most of the related literature. All insights are carefully validated through numerical simulations.

A secondary EWMA-based dictionary learning algorithm for polynomial phase signal denoising

Under the influence of additive white Gaussian noise, sparse representation cannot effectively remove noise associated with the polynomial phase signal (PPS) via most dictionary learning algorithms whose training data come from the noisy signal, such as K-SVD and RLS-DLA. In this paper, we present a novel dictionary learning algorithm based on secondary exponentially weighted moving average (SEWMA) to denoise PPS. In the proposed algorithm, we first estimate the signal-to-noise (SNR) of the PPS to set the optimal rate of a weighted decline using covariance matrix model. Second we use RLS-DLA to train the dictionary. Thirdly, SEWMA is used to refine atoms in the learned dictionary. In this way, the SNR of the reconstructed signal obtained using the proposed algorithm is clearly higher than that of other algorithms, whereas the mean squared error is lower than that of other algorithms. To obtain the optimal denoising performance, the optimal rate of a weighted decline is set based on the estimated SNR. Simulation results show that the proposed method outperforms the K-SVD, RLS-DLA in mean square error and the SNR.

A Novel Sparse Bayesian Space-Time Adaptive Processing Algorithm to Mitigate Off-Grid Effects

Space-time adaptive processing (STAP) algorithms based on sparse recovery (SR) have been researched because of their low requirement of training snapshots. However, once some portion of clutter is not located on the grids, i.e., off-grid problems, the performances of most SR-STAP algorithms degrade significantly. Reducing the grid interval can mitigate off-grid effects, but brings strong column coherence of the dictionary, heavy computational load, and heavy storage load. A sparse Bayesian learning approach is proposed to mitigate the off-grid effects in the paper. The algorithm employs an efficient sequential addition and deletion of dictionary atoms to estimate the clutter subspace, which means that strong column coherence has no effect on the performance of the proposed algorithm. Besides, the proposed algorithm does not require much computational load and storage load. Off-grid effects can be mitigated with the proposed algorithm when the grid-interval is sufficiently small. The excellent performance of the novel algorithm is demonstrated on the simulated data.

Power Quality Data Compression and Disturbances Recognition Based on Deep CS-BiLSTM Algorithm With Cloud-Edge Collaboration

The current disturbance classification of power quality data often has the problem of low disturbance recognition accuracy due to its large volume and difficult feature extraction. This paper proposes a hybrid model based on distributed compressive sensing and a bi-directional long-short memory network to classify power quality disturbances. A cloud-edge collaborative framework is first established with distributed compressed sensing as an edge-computing algorithm. With the uploading of dictionary atoms of compressed sensing, the data transmission and feature extraction of power quality is achieved to compress power quality measurements. In terms of data transmission and feature extraction, the dictionary atoms and measurements uploaded at the edge are analyzed in the cloud by building a cloud-edge collaborative framework with distributed compressed sensing as the edge algorithm so as to achieve compressed storage of power quality data. For power disturbance identification, a new network structure is designed to improve the classification accuracy and reduce the training time, and the training parameters are optimized using the Deep Deterministic Policy Gradient algorithm in reinforcement learning to analyze the noise immunity of the model under different scenarios. Finally, the simulation analysis of 10 common power quality disturbance signals and 13 complex composite disturbance signals with random noise shows that the proposed method solves the problem of inadequate feature selection by traditional classification algorithms, improves the robustness of the model, and reduces the training time to a certain extent.

A Smart Noise Jamming Suppression Method Based on Atomic Dictionary Parameter Optimization Decomposition

Smart noise jamming is a new jamming style against radar, which plays an important role in modern radar electronic warfare. In order to solve the complex problem of convolutional smart noise jamming suppression with different time delay and jamming frequency modulation, a novel jamming suppression method based on the optimized atomic dictionary decomposition by estimating significant jamming parameters is proposed in this paper. First, the dual channel jamming signal information is obtained by designing twinning waveforms, then the independent estimation of time delay and jamming frequency parameters are established based on the spatial position sequences of the false targets. After that, the atomic dictionary is optimized by utilizing the obtained jamming parameters to achieve more effective decomposition. The performance of the new jamming suppression method is analyzed and verified by experimental simulations. The results show that this method can feasibly and practicably suppress the smart noise jamming with a deceptive effect, and the atomic decomposition efficiency is highly improved.

Class Specific Dictionary Learning with the Independence Between-class and Dependence Intra-class Coefficient’s Constraint

In the field of image classification, deep learning has become the focus of research. But when the number of training samples is small, especially when there are a large number of intra-class variations in the small samples, the performance of deep learning is often not satisfactory. To deal with the problem, a new dictionary learning method based on sparse representation and an improved coefficient’s constraint is proposed. A general dictionary is learned to eliminate noise signal, and then based on the general dictionary, a class specific dictionary is learned by an improved coefficient’s constraint which maintaining the independence of the dictionary atoms between-classes, while allowing the dependence of the dictionary atoms intra- class. The class specific dictionary combined with the general dictionary is used for the image recognition. Experimental results show that, compared with the state-of-the-art dictionary learning methods, the proposed method usually shows better performance on image classification with small data sets.