Sparse Representation Research Articles

An Effective and Lightweight Full-Scale Target Detection Network for UAV Images Based on Deformable Convolutions and Multi-Scale Contextual Feature Optimization

Currently, target detection on unmanned aerial vehicle (UAV) images is a research hotspot. Due to the significant scale variability of targets and the interference of complex backgrounds, current target detection models face challenges when applied to UAV images. To address these issues, we designed an effective and lightweight full-scale target detection network, FSTD-Net. The design of FSTD-Net is based on three principal aspects. Firstly, to optimize the extracted target features at different scales while minimizing background noise and sparse feature representations, a multi-scale contextual information extraction module (MSCIEM) is developed. The multi-scale information extraction module (MSIEM) in MSCIEM can better capture multi-scale features, and the contextual information extraction module (CIEM) in MSCIEM is designed to capture long-range contextual information. Secondly, to better adapt to various target shapes at different scales in UAV images, we propose the feature extraction module fitting different shapes (FEMFDS), based on deformable convolutions. Finally, considering low-level features contain rich details, a low-level feature enhancement branch (LLFEB) is designed. The experiments demonstrate that, compared to the second-best model, the proposed FSTD-Net achieves improvements of 3.8%, 2.4%, and 2.0% in AP50, AP, and AP75 on the VisDrone2019, respectively. Additionally, FSTD-Net achieves enhancements of 3.4%, 1.7%, and 1% on the UAVDT dataset. Our proposed FSTD-Net has better detection performance compared to state-of-the-art detection models. The experimental results indicate the effectiveness of the FSTD-Net for target detection in UAV images.

A Euclidean transformer for fast and stable machine learned force fields

Recent years have seen vast progress in the development of machine learned force fields (MLFFs) based on ab-initio reference calculations. Despite achieving low test errors, the reliability of MLFFs in molecular dynamics (MD) simulations is facing growing scrutiny due to concerns about instability over extended simulation timescales. Our findings suggest a potential connection between robustness to cumulative inaccuracies and the use of equivariant representations in MLFFs, but the computational cost associated with these representations can limit this advantage in practice. To address this, we propose a transformer architecture called SO3krates that combines sparse equivariant representations (Euclidean variables) with a self-attention mechanism that separates invariant and equivariant information, eliminating the need for expensive tensor products. SO3krates achieves a unique combination of accuracy, stability, and speed that enables insightful analysis of quantum properties of matter on extended time and system size scales. To showcase this capability, we generate stable MD trajectories for flexible peptides and supra-molecular structures with hundreds of atoms. Furthermore, we investigate the PES topology for medium-sized chainlike molecules (e.g., small peptides) by exploring thousands of minima. Remarkably, SO3krates demonstrates the ability to strike a balance between the conflicting demands of stability and the emergence of new minimum-energy conformations beyond the training data, which is crucial for realistic exploration tasks in the field of biochemistry.

Extended fiducial inference: toward an automated process of statistical inference

Abstract While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set—‘inferring the uncertainty of model parameters on the basis of observations’—has been continually pursued by many statisticians. To this end, we develop a new statistical inference method called extended Fiducial inference (EFI). The new method achieves the goal of fiducial inference by leveraging advanced statistical computing techniques while remaining scalable for big data. Extended Fiducial inference involves jointly imputing random errors realized in observations using stochastic gradient Markov chain Monte Carlo and estimating the inverse function using a sparse deep neural network (DNN). The consistency of the sparse DNN estimator ensures that the uncertainty embedded in observations is properly propagated to model parameters through the estimated inverse function, thereby validating downstream statistical inference. Compared to frequentist and Bayesian methods, EFI offers significant advantages in parameter estimation and hypothesis testing. Specifically, EFI provides higher fidelity in parameter estimation, especially when outliers are present in the observations; and eliminates the need for theoretical reference distributions in hypothesis testing, thereby automating the statistical inference process. Extended Fiducial inference also provides an innovative framework for semisupervised learning.

A Point Cloud Improvement Method for High-Resolution 4D mmWave Radar Imagery

To meet the requirement of autonomous driving development, high-quality point cloud generation of the environment has become the focus of 4D mmWave radar development. On the basis of mass producibility and physical verifiability, a design method for improving the quality and density of point cloud imagery is proposed in this paper, including antenna design, array design, and the dynamic detection method. The utilization of apertures is promoted through antenna design and sparse MIMO array optimization using the genetic algorithm (GA). The hybrid strategy for complex point clouds is adopted using the proposed dynamic CFAR algorithm, which enables dynamic adjustment of the threshold by discriminating and calculating different scanning regions. The effectiveness of the proposed method is verified by simulations and practical experiments. Aiming at system manufacture, analysis methods for the ambiguity function (AF) and shooting and bouncing rays (SBR) tracing are introduced, and an mmWave radar system is realized based on the proposed method, with its performance proven by practical experiments.

Introducing an indoor object classification dataset including sparse point clouds from mmWave radar

This document introduces the RadIOCD, which is a dataset that contains sparse point cloud representations of indoor objects, collected by subjects wearing a commercial off-the-shelf mmWave radar. In particular, RadIOCD includes the recordings of 10 volunteers moving towards 5 different objects (i.e., backpack, chair, desk, human, and wall), placed in 3 different environments. RadIOCD includes sparse 3D point cloud data, together with their doppler velocity and intensity provided by the mmWave radar. A total of 5,776 files are available, with each one having an approximate duration of 8s. The scope of RadIOCD is the availability of data for the recognition of objects solely recorded by the mmWave radar, to be used in applications were the vision-based classification is cumbersome though critical (e.g., in search and rescue operation where there is smoke inside a building). Furthermore, we showcase that this dataset after being segmented into 76,821 samples contains enough data to apply Machine Learning-based techniques, ensuring that they could generalize in different environments and “unseen“ subjects.

On the emerging potential of quantum annealing hardware for combinatorial optimization

Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies have indicated that quantum annealing hardware does not provide an irrefutable performance gain over state-of-the-art optimization methods. However, as this hardware continues to evolve, each new iteration brings improved performance and warrants further benchmarking. To that end, this work conducts an optimization performance assessment of D-Wave Systems’ Advantage Performance Update computer, which can natively solve sparse unconstrained quadratic optimization problems with over 5,000 binary decision variables and 40,000 quadratic terms. We demonstrate that classes of contrived problems exist where this quantum annealer can provide run time benefits over a collection of established classical solution methods that represent the current state-of-the-art for benchmarking quantum annealing hardware. Although this work does not present strong evidence of an irrefutable performance benefit for this emerging optimization technology, it does exhibit encouraging progress, signaling the potential impacts on practical optimization tasks in the future.

Dominant duct azimuthal acoustic mode detection considering failed wall-installed microphones with amplitude or phase measurement biases

Reliable duct mode detection results are essential for aero-engine health condition monitoring and low-noise design. Harsh aero-engine measurement environments may cause biases in amplitude and phase measurements due to the failure of wall-mounted microphones, which will decrease the performance of advanced sparse representation algorithms for duct mode detection. In this paper, two strategies to detect the duct mode with the failed microphones are proposed. An optimization problem is constructed considering the low-rankness of theoretical array measurement and row-sparsity of the failed microphone measurements. The Strategy 1 is based on the recovery of the theoretical array measurement. The recovered array measurement can be further used to detect the duct mode via the sparsity-induced duct mode detection algorithm (generalized minimax-concave penalty in this paper). With the simulation, the Strategy 1 can not recover the theoretical array measurement completely. The Strategy 2 is based on the removal of the failed microphone measurements. With the simulation and experiment, it turns out that the Strategy 2 can detect the interested mode accurately.

Deep Learing for Sparse Domain Kalman Filtering With Applications on ECG Denoising and Motility Estimation.

The reconstruction of an input based on a sparse combination of signals, known as sparse coding, has found widespread use in signal processing. In this work, the combination of sparse coding with Kalman filtering is explored and its potential is shown on two use-cases. This work extends the Iterative Shrinkage and Thresholding Algorithm with a Kalman filter in the sparse domain. The resulting method may be implemented as a deep unfolded neural network and may be applied to any signal which has a sparse representation and a known or assumed relation between consecutive measurements. This method is evaluated on the use cases of noise reduction in the electrocardiogram (ECG) and the estimation of object motility. For ECG denoising, the proposed method achieved an improvement in Signal-to-Noise ratio of 18.6 dB, which is comparable to state-of-the-art. In motility estimation, a correlation of 0.84 with ground truth simulations was found. The proposed method was shown to have advantages over sparse coding and Kalman filtering alone. Due to the low complexity and high generalizability of the proposed method, the implementation of context-specific knowledge or an extension to other applications can be readily made. The presented Kalman-ISTA algorithm is a resource-efficient method combining the promise of both sparse coding and Kalman filtering, making it well-suited for various applications.

Sparse Graph Representation Learning Based on Reinforcement Learning for Personalized Mild Cognitive Impairment (MCI) Diagnosis.

Resting-state functional magnetic resonance imaging (rs-fMRI) has gained attention as a reliable technique for investigating the intrinsic function patterns of the brain. It facilitates the extraction of functional connectivity networks (FCNs) that capture synchronized activity patterns among regions of interest (ROIs). Analyzing FCNs enables the identification of distinctive connectivity patterns associated with mild cognitive impairment (MCI). For MCI diagnosis, various sparse representation techniques have been introduced, including statistical- and deep learning-based methods. However, these methods face limitations due to their reliance on supervised learning schemes, which restrict the exploration necessary for probing novel solutions. To overcome such limitation, prior work has incorporated reinforcement learning (RL) to dynamically select ROIs, but effective exploration remains challenging due to the vast search space during training. To tackle this issue, in this study, we propose an advanced RL-based framework that utilizes a divide-and-conquer approach to decompose the FCN construction task into smaller sub-problems in a subject-specific manner, enabling efficient exploration under each sub-problem condition. Additionally, we leverage the learned value function to determine the sparsity level of FCNs, considering individual characteristics of FCNs. We validate the effectiveness of our proposed framework by demonstrating its superior performance in MCI diagnosis on publicly available cohort datasets.

Sparse Flow Sensor Placement Optimization for Flight-by-Feel Control of 2D Airfoils

This research introduces the Sparse Sensor Placement Optimization for Prediction algorithm and explores its use in bioinspired flight-by-feel control system design. Flying animals have velocity-sensing structures on their wings and are capable of highly agile flight in unsteady conditions, a proof-of-concept that artificial flight-by-feel control systems may be effective. Constrained by size, weight, and power, a flight-by-feel sensory system should have the fewest optimally placed sensors which capture enough information to predict the flight state. Flow datasets, such as from computational fluid dynamics, are discrete, often highly discontinuous, and ill-suited for conventional sensor placement optimization techniques. The data-driven Sparse Sensor Placement Optimization for Prediction approach reduces high-dimensional flow data to a low-dimensional sparse approximation containing nearly all of the original information, thereby identifying a near-optimal placement for any number of sensors. For two or more airflow velocity magnitude sensors, this algorithm finds a placement solution (design point) which predicts angle of attack of airfoils to within 0.10° and ranks within the top 1% of all possible design points validated by combinatorial search. The scalability and adaptability of this algorithm is demonstrated on several 2D model variations in clean and noisy data, and model sensitivities are evaluated and compared against conventional optimization techniques. Applications for this sensor placement algorithm are explored for aircraft design, flight control, and beyond.

Randomized algorithms for large-scale dictionary learning

Dictionary learning is an important sparse representation algorithm which has been widely used in machine learning and artificial intelligence. However, for massive data in the big data era, classical dictionary learning algorithms are computationally expensive and even can be infeasible. To overcome this difficulty, we propose new dictionary learning methods based on randomized algorithms. The contributions of this work are as follows. First, we find that dictionary matrix is often numerically low-rank. Based on this property, we apply randomized singular value decomposition (RSVD) to the dictionary matrix, and propose a randomized algorithm for linear dictionary learning. Compared with the classical K-SVD algorithm, an advantage is that one can update all the elements of the dictionary matrix simultaneously. Second, to the best of our knowledge, there are few theoretical results on why one can solve the involved matrix computation problems inexactly in dictionary learning. To fill-in this gap, we show the rationality of this randomized algorithm with inexact solving, from a matrix perturbation analysis point of view. Third, based on the numerically low-rank property and Nyström approximation of the kernel matrix, we propose a randomized kernel dictionary learning algorithm, and establish the distance between the exact solution and the computed solution, to show the effectiveness of the proposed randomized kernel dictionary learning algorithm. Fourth, we propose an efficient scheme for the testing stage in kernel dictionary learning. By using this strategy, there is no need to form nor store kernel matrices explicitly both in the training and the testing stages. Comprehensive numerical experiments are performed on some real-world data sets. Numerical results demonstrate the rationality of our strategies, and show that the proposed algorithms are much efficient than some state-of-the-art dictionary learning algorithms. The MATLAB codes of the proposed algorithms are publicly available from https://github.com/Jiali-yang/RALDL_RAKDL.

Sparse graphs-based dynamic attention networks

In previous research, the prevailing assumption was that Graph Neural Networks (GNNs) precisely depicted the interconnections among nodes within the graph's architecture. Nonetheless, real-world graph datasets are often rife with noise, elements that can disseminate through the network and ultimately affect the outcome of the downstream tasks. Facing the complex fabric of real-world graphs and the myriad potential disturbances, we introduce the Sparse Graph Dynamic Attention Networks (SDGAT) in this research. SDGAT employs the L0 regularization technique to achieve a sparse representation of the graph structure, which eliminates noise and generates a more concise sparse graph. Building upon this foundation, the model integrates a dynamic attention mechanism, allowing it to selectively focus on key nodes and edges, filter out irrelevant data, and simultaneously facilitate effective feature aggregation with important neighbors. To evaluate the performance of SDGAT, we conducted experiments on three citation datasets and compared its performance against commonly employed models. The outcomes indicate that SDGAT excels in node classification tasks, notably on the Cora dataset, with an accuracy rate of 85.29%, marking a roughly 3% enhancement over the majority of baseline models. The experimental findings provide evidence that SDGAT delivers effective performance on all three citation datasets, underscoring the efficacy of the dynamic attention network built upon a sparse graph.

Improved Sparse Representation of Image from Inferred Angles of Steerable Wavelet

Objectives: Presenting images with sparse coefficients has a wide variety of real-time applications in compressive sensing. However, sparse representations of images present challenges due hidden similarities in the higher order moments. Literature suggests that the applications that involve natural images present a high level of similarity. Steerable basis, due to their rotational invariant property, have shown potential in sparse representation of natural images. Hence, the objective of the proposed study is to identify steerable basis that maximize the sparse representation of natural images. Method: Prior studies have used the angle of steerable basis either from the random assignment or derived from Hough transform. In this study, we propose the selection of steerable basis angle derived from maximum a prior method. Exploiting a steerable basis for better sparse representation requires the knowledge of proper steerable angles. Hence, we propose using MAP learning approach to identify this angle. Findings: The proposed method resulted in optimal steerable angle without the need for calculation of Hough Transform. In addition, the method also resulted in almost 10 percent improvement in sparse representation as indicated by higher Kurtosis. Novelty: We compare the measure of sparsity to evaluate the effectiveness of the proposed method. The results indicate the optimal sparsity from the proposed method as indicated from the maximum values of kurtosis compared to the previous related methods. In addition, the proposed method relaxes the requirement of manipulating Hough transform for optimal steerable angle. Keywords: Sparsity, Steerable Basis, Wavelet Pyramid Structure, Image Compression, Hough Transform

Research and Application of Destriping Algorithm based on Weighted Block Sparse Representation to FengYun Satellite Imager Data

Abstract In remote sensing imaging systems, stripe noise is a pervasive issue primarily caused by the inconsistent response of multiple detectors. Stripe noise not only affects image quality but also severely hinders subsequent quantitative derived products and applications. Therefore, it is crucial to eliminate stripe noise while preserving detailed structure information in order to enhance image quality. Although existing destriping methods have achieved certain effects to some extent, they still face problems such as loss of image details, image blur, and ringing artifacts. To address these issues, this study proposes an image stripe correction algorithm based on weighted block sparse representation. This research applies techniques such as differential low-rank constraint and edge weight factor to remove stripe noise while retaining image detail information. The algorithm also uses the alternating direction method of multipliers (ADMM) to solve the MCP regularized least squares optimization problem model, improving the processing efficiency of the model. The results of this study have been applied and validated in imager data from the Medium Resolution Spectral Imager (MERSI-II) onboard FengYun-3D satellite, the Multi-channel Scanning Radiometer (AGRI) onboard FengYun-4A satellite and Precipitation Microwave Radiometer (MWRI–RM) onboard FengYun-3G. Compared to typical stripe correction methods, the proposed method achieves better stripe removal while preserving image detail information. The destriped image data can be used to generate high-quality quantitative products for various applications. Overall, by combining insights from prior research and innovative techniques, this study provides a more effective and robust solution to the stripe noise problem in remote sensing and weather forecast.

System identification based on sparse approximation of Koopman operator

System identification based on sparse approximation of Koopman operator

Accelerated Simulation of Multi-Electrode Arrays Using Sparse and Low-Rank Matrix Techniques.

Modeling of Multi-Electrode Arrays used in neural stimulation can be computationally challenging since it may involve incredibly dense circuits with millions of interconnected resistors, representing current pathways in an electrolyte (resistance matrix), coupled to nonlinear circuits of the stimulating pixels themselves. Here, we present a method for accelerating the modeling of such circuits while minimizing the error of a simplified simulation by using a sparse plus low-rank approximation of the resistance matrix. Specifically, we prove that thresholding of the resistance matrix elements enables its sparsification with minimized error. This is accomplished with a sorting algorithm implying efficient O (N log (N)) complexity. The eigenvalue-based low-rank compensation then helps achieve greater accuracy without adding significantly to the problem size. Utilizing these matrix techniques, we accelerated the simulation of multi-electrode arrays by an order of magnitude, reducing the computation time by about 10-fold, while maintaining an average error of less than 0.3% in the current injected from each electrode. We also show a case where acceleration reaches at least 133 times with additional error in the range of 4%, demonstrating the ability of this algorithm to perform under extreme conditions. Although the techniques presented here are used for simulations of photovoltaic retinal prostheses, they are also immediately applicable to any circuit involving dense connections between nodes, and, with modifications, more generally to any systems involving non-sparse matrices. This approach promises significant improvements in the efficiency of modeling the next-generation retinal implants having thousands of pixels, enabling iterative design with broad applicability.

Optimal Transport with Constraints: From Mirror Descent to Classical Mechanics.

Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is limited by the lack of principled and flexible ways to incorporate realistic constraints. We propose a principled physics-based approach to impose constraints flexibly in optimal transport problems. Constraints are included in mirror descent dynamics using the D'Alembert-Lagrange principle from classical mechanics. This results in a sparse, local and linear approximation of the feasible set leading in many cases to closed-form updates.

LDCT image denoising algorithm based on two-dimensional variational mode decomposition and dictionary learning

Low-dose X-CT scanning method effectively reduces radiation hazards, however, reducing the radiation dose will introduce noise and artifacts during the projection process, resulting in a decrease in the quality of the reconstructed image. To address this problem, we combined 2D variational modal decomposition and dictionary learning. We proposed a low-dose CT (LDCT) image denoising algorithm based on an improved K-SVD algorithm with image decomposition. The dictionary obtained by K-SVD training lacks consideration of image structure information. To address this problem, we employ the two-dimensional variational mode decomposition (2D-VMD) method to decompose the image into distinct modal components. Through the adaptive learning of dictionaries based on the characteristics of each modal component, independent denoising processing is applied to each component, avoiding the loss of structural and detailed information in the image. In addition, we introduce the regularized orthogonal matching pursuit algorithm (ROMP) and dictionary atom optimization method to improve the sparse representation ability of the dictionary and reduce the impact of noise atoms on denoising performance. The experiments show that the proposed method outperforms other denoising methods regarding peak signal-to-noise ratio and structural similarity. The proposed method maintains the denoised image details and structural information while removing LDCT image noise and artifacts. The image quality after denoising is significantly improved and facilitates more accurate detection and analysis of lesion areas.

High-resolution seismic inversion method based on joint data-driven in the time-frequency domain

Seismic inversion can be divided into time-domain inversion and frequency-domain inversion based on different transform domains. Time-domain inversion has stronger stability and noise resistance compared to frequency-domain inversion. Frequency domain inversion has stronger ability to identify small-scale bodies and higher inversion resolution. Therefore, the research on the joint inversion method in the time-frequency domain is of great significance for improving the inversion resolution, stability, and noise resistance. The introduction of prior information constraints can effectively reduce ambiguity in the inversion process. However, the existing model-driven time-frequency joint inversion assumes a specific prior distribution of the reservoir. These methods do not consider the original features of the data and are difficult to describe the relationship between time-domain features and frequency-domain features. Therefore, this paper proposes a high-resolution seismic inversion method based on joint data-driven in the time-frequency domain. The method is based on the impedance and reflectivity samples from logging, using joint dictionary learning to obtain adaptive feature information of the reservoir, and using sparse coefficients to capture the intrinsic relationship between impedance and reflectivity. The optimization result of the inversion is achieved through the regularization term of the joint dictionary sparse representation. We have finally achieved an inversion method that combines constraints on time-domain features and frequency features. By testing the model data and field data, the method has higher resolution in the inversion results and good noise resistance.

A novel weighted sparse classification framework with extended discriminative dictionary for data-driven bearing fault diagnosis

Dictionary learning has emerged as an effective approach for data-driven fault diagnosis due to its strong sparse representation ability. Nevertheless, the gathered vibration signals always exhibit a time-shift phenomenon, greatly diminishing the representation capability of dictionary learning methods. Besides, in real-world industrial scenarios, where heavy noise as common features inevitably cover the discriminative features, the decline in the recognition performance of data-driven fault diagnosis methods is a critical challenge. In this paper, a novel weighted sparse classification framework with extended discriminative dictionary (WSC-EDD) is proposed. First, an extended discriminative dictionary design strategy is developed to construct generalized-domain extended dictionary model with strong representation and discrimination ability, in which a novel generalized-domain dictionary fusion method is developed to reduce the effect of time-shift phenomenon and enhance the representation ability of the dictionary. Further, generalized-domain discriminative sub-dictionaries are optimized by the K-singular value decomposition in a data-driven fashion and then the whole extension dictionary are designed adaptively. Second, a weighted optimization method is developed to highlight the contribution of non-zero elements in the correct projection region in sparse codes, in which weighted diagonal matrices are designed. Finally, a sparse recognition method is established for bearing fault classification. The experiment results on three challenging bearing datasets demonstrate that the proposed framework yields average diagnosis accuracies of 99.75%, 99.93% and 100%, respectively. Moreover, the superiority and robustness of WSC-EDD are further confirmed by comparing with several competing methods.