Sparse Representation Research Articles

Technical note: Optimizing spot-scanning proton arc therapy with a novel spot sparsity approach.

One of the main challenges of utilizing spot-scanning proton arc therapy (SPArc) in routine clinics is treatment delivery efficiency. Spot reduction, which relies on spot sparsity optimization (SSO), is crucial for achieving high delivery efficiency inSPArc. This study aims to develop a novel SSO approach based on the alternating directions method of multipliers (ADMM) for SPArc to achieve high treatment delivery efficiency and maintain optimal dosimetric planquality. In this study, SSO for SPArc is based on the least-square dose fidelity term with L0-norm regularization. The novel optimization approach is based on the ADMM framework, in which the minimum monitor unit constraint was considered to improve the plan quality. A state-of-the-art SSO method, the primal-dual active set with continuation (PDASC) algorithm published previously, was utilized as a benchmark. Two SPArc plan groups with the same beam assignment and clinical constraint were generated, in which the former group was SPArc plan with SSO utilizing ADMM, denoted as , and the later group was SPArc with SSO utilizing PDASC, denoted as . Nine clinical cases included five different cancer sites (brain, lung, liver, prostate, and head&neck cancer) were used. The SSO method's performance was evaluated in terms of spot sparsity level (the number of zero-valued elements divided by the total number of elements), beam delivery time, dosimetric plan quality, and plan robustness. Compared to the plan, the plan exhibits superior sparsity and higher delivery efficiency while maintaining good planquality. This study introduces a novel spot sparsity optimization approach using the ADMM framework to improve the delivery efficiency of SPArc. Compared to the existing state-of-the-art SSO method, such an approach could further enhance delivery efficiency while maintaining good plan quality, which could promote the implementation of SPArc in theclinic's.

Accelerated multi-kernel sparse stochastic optimization classifier algorithm for explainable prediction

Accelerated multi-kernel sparse stochastic optimization classifier algorithm for explainable prediction

Analysis for sparse channel representation based on dictionary learning in massive MIMO systems

AbstractThe accuracy analysis of dictionary sparse representation for channels in massive MIMO systems is a relatively unexplored field. Existing research has primarily focused on investigating the accuracy of dictionary sparse representation using simulation in massive MIMO systems, but has not provided quantitative accuracy analysis. To address this gap, the correlation numerical proportional factor is proposed to represent the accuracy performance of non‐zero elements in the coefficient matrix. Additionally, a qualitative analytical formula for dictionary sparse representation accuracy is provided and an optimal upper bound for the correlation numerical proportional factor is established. Furthermore, the innovation indicates that the accuracy of dictionary sparse representation is mainly influenced by the cross‐correlation between the pilots matrix and the dictionary matrix, as well as sparsity. The author has also developed a method for minimizing the correlation numerical proportional factor. In order to obtain an optimal sparse representation coefficient matrix, a cross‐correlation matrix is constructed and an analytical expression is derived for it as well as its use as an optimal hard decision threshold is determined. Finally, a sparse representation coefficient optimization algorithm is proposed using this optimal threshold. Simulation results demonstrate that this algorithm can significantly improve channel sparse dictionary representation accuracy.

Efficient Data Processing Pipeline for Event-Based Vision Datasets: Techniques and Insights

Abstract Event-based vision datasets have emerged as a critical asset in advancing the capabilities of real-time perception systems, particularly in fields such as robotics, autonomous vehicles, and human-computer interaction. These datasets enable low-latency processing by capturing asynchronous, pixel-level changes in the scene, providing a distinct advantage over traditional frame-based systems. However, the diverse formats and characteristics of event-based datasets pose significant challenges for efficient processing and analysis, hindering their broader adoption and integration. In this paper, we present a versatile and comprehensive data processing pipeline designed to address these challenges by supporting multiple event-data formats, including newer formats such as EVT2 and EVT3. This pipeline not only converts data into widely supported formats like AEDAT and NPZ, but also ensures that the unique characteristics of event-based data—such as temporal precision and sparse event representation—are preserved throughout the conversion process. By applying this pipeline to several open-source datasets, we establish a standardized, efficient methodology for dataset manipulation that enhances compatibility and reproducibility in event-based vision research. Additionally, we introduce a novel high-resolution event-based action dataset, converted into various formats using our pipeline, which opens new avenues for exploring event-based techniques in action recognition. This dataset and our pipeline serve as valuable resources for the research community, enabling advancements in real-time vision applications and fostering greater collaboration and standardization across studies.

Digital Dark Field-Higher Contrast and Greater Specificity Dark Field Imaging Using a 4DSTEM Approach.

A new method for dark field imaging is introduced, which uses scanned electron diffraction (or 4DSTEM-4-dimensional scanning transmission electron microscopy) datasets as its input. Instead of working on simple summation of intensity, it works on a sparse representation of the diffraction patterns in terms of a list of their diffraction peaks. This is tested on a thin perovskite film containing structural ordering resulting in additional superlattice spots that reveal details of domain structures, and is shown to give much better selectivity and contrast than conventional virtual dark field imaging. It is also shown to work well in polycrystalline aggregates of CuO nanoparticles. In view of the higher contrast and selectivity, and the complete exclusion of diffuse scattering from the image formation, it is expected to be of significant benefit for characterization of a wide variety of crystalline materials.

Alternative Learning Paradigms for Image Quality Transfer

Image Quality Transfer (IQT) aims to enhance the contrast and resolution of low-quality medical images, e.g. obtained from low-power devices, with rich information learned from higher quality images. In contrast to existing IQT methods in the literature which adopt supervised learning frameworks, in this work, we propose two novel formulations of the IQT problem. The first approach uses an unsupervised learning framework, whereas the second is a combination of both supervised and unsupervised learning. The unsupervised learning approach considers a sparse representation (SRep) and dictionary learning model, which we call IQT-SRep, whereas the combination of supervised and unsupervised learning ap- proach is based on deep dictionary learning (DDL), which we call IQT-DDL. The IQT-SRep approach trains two dictionaries using a sparse representation model using pairs of low- and high-quality volumes. Subsequently, the sparse representation of a low-quality block, in terms of the low-quality dictionary, can be directly used to recover the corresponding high-quality block using the high-quality dictionary. On the other hand, the IQT-DDL ap- proach explicitly learns a high-resolution dictionary to upscale the input volume, while the entire network, including high dictionary generator, is simultaneously optimised to take full advantage of deep learning methods. The two models are evaluated using a low-field mag- netic resonance imaging (MRI) application aiming to recover high-quality images akin to those obtained from high-field scanners. Experiments comparing the proposed approaches against state-of-the-art supervised deep learning IQT method (IQT-DL) identify that the two novel formulations of the IQT problem can avoid bias associated with supervised meth- ods when tested using out-of-distribution data that differs from the distribution of the data the model was trained on. This highlights the potential benefit of these novel paradigms for IQT.

Sparse representation-based noise reduction for BOTDR monitoring signals in foundation pit anchor cables

Abstract In foundation pit monitoring, the Brillouin optical time-domain reflectometer (BOTDR) system typically has a low signal-to-noise ratio (SNR). To solve this problem, a BOTDR signal noise-suppression method based on sparse representation is proposed in this paper. The initial dictionary is constructed from the eigenvectors of the normalized graph Laplace matrix, and K-SVD and OMP algorithms are combined to update the dictionary and coefficient matrix to sparsely represent the essential characteristics of the BOTDR signal, filtering out random noise lacking sufficient similarity data and improving the quality of the reconstructed signal. To verify the effectiveness of the proposed algorithm, a BOTDR temperature-sensing experimental system was designed and used to test the denoising performance of the sparse representation algorithm quantitatively. The experimental results showed that the average SNR of the algorithm on six temperature levels was 27.4%, 15.4%, 13.1%, and 17.9% higher than that of WDD, EMT, EMD, and the raw signals, respectively. The average sample entropy (SE) was 24.4%, 16.0%, 15.4%, and 47.9% lower than that of WDD, EMT, EMD, and the raw signals, respectively. Additionally, the proposed Laplace-based dictionary outperformed the DCT dictionary. Finally, the monitoring project of the Beijing Stomatological Hospital was used as a test site. The sparse representation algorithm was used to conduct noise reduction experiments on the on-site anchor cable fiber optic monitoring signals. The average signal SE decrease of monitoring signals at the site reached 45.2%. This study provides an effective signal denoising method for the application of BOTDR technology in foundation pit monitoring.

Forest Fire Burn Scar Mapping Based on Modified Image Super-Resolution Reconstruction via Sparse Representation

Forest Fire Burn Scar Mapping Based on Modified Image Super-Resolution Reconstruction via Sparse Representation

ICe: interior cevian initialization for enhanced reconstruction methods

This paper introduces two novel self-induced basis strategies, interior cevian initialization for orthogonal matching pursuit (ICe) and its l2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_2$$\\end{document}-sense optimized version, optimized interior cevian initialization (OICe). These methods address the complexity and convergence issues of the previously proposed self-inspired bases (SIBS) approach. Both algorithms enhance sparse image representation by generating adaptive auxiliary atoms tailored to the image, thereby improving reconstruction quality and computational efficiency. Experimental results show that ICe achieves up to a 35.6% improvement in Normalized Mean Squared Error (NMSE) and a 16.4% increase in Structural Similarity Index (SSIM) compared to conventional OMP. OICe, as the l2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_2$$\\end{document}-sense optimized version of ICe, delivers even greater performance, with improvements of up to 40% in NMSE and 18.5% in SSIM. Additionally, both ICe and OICe significantly reduce bits per pixel (BPP) for image encoding, outperforming SIBS when paired with state-of-the-art dictionaries such as KSVD, MOD, RBDL, and ODL. These results highlight the effectiveness of ICe and OICe in addressing key challenges in sparse representation, offering enhanced accuracy and efficiency across a variety of applications.

High-Dimensional Block Diagonal Covariance Structure Detection Using Singular Vectors

The assumption of independent subvectors arises in many aspects of multivariate analysis. In most real-world applications, however, we lack prior knowledge about the number of subvectors and the specific variables within each subvector. Yet, testing all these combinations is not feasible. For example, for a data matrix containing 15 variables, there are already 1 382 958 545 possible combinations. Given that zero correlation is a necessary condition for independence, independent subvectors exhibit a block diagonal covariance matrix. This paper focuses on the detection of such block diagonal covariance structures in high-dimensional data and therefore also identifies uncorrelated subvectors. Our approach exploits the fact that the structure of the covariance matrix is mirrored by the structure of its eigenvectors. However, the true block diagonal structure is masked by noise in the sample case. To address this problem, we propose to use sparse approximations of the sample eigenvectors to reveal the sparse structure of the population eigenvectors. Notably, the right singular vectors of a data matrix with an overall mean of zero are identical to the sample eigenvectors of its covariance matrix. Using sparse approximations of these singular vectors instead of the eigenvectors makes the estimation of the covariance matrix obsolete. We demonstrate the performance of our method through simulations and provide real data examples. Supplementary materials for this article are available online.

Simultaneous image denoising and completion through convolutional sparse representation and nonlocal self-similarity

Low rank matrix approximation (LRMA) has been widely studied due to its capability of approximating original image from the degraded image. According to the characteristics of degraded images, image denoising and image completion have become research objects. Existing methods are usually designed for a single task. In this paper, focusing on the task of simultaneous image denoising and completion, we propose a weighted low rank sparse representation model and the corresponding efficient algorithm based on LRMA. The proposed method integrates convolutional analysis sparse representation (ASR) and nonlocal statistical modeling to maintain local smoothness and nonlocal self-similarity (NLSM) of natural images. More importantly, we explore the alternating direction method of multipliers (ADMM) to solve the above inverse problem efficiently due to the complexity of simultaneous image denoising and completion. We conduct experiments on image completion for partial random samples and mask removal with different noise levels. Extensive experiments on four datasets, i.e., Set12, Kodak, McMaster, and CBSD68, show that the proposed method prevents the transmission of noise while completing images and has achieved better quantitative results and human visual quality compared to 17 methods. The proposed method achieves (1.9%, 1.8%, 4.2%, and 3.7%) gains in average PSNR and (4.2%, 2.9%, 6.7%, and 6.6%) gains in average SSIM over the sub-optimal method across the four datasets, respectively. We also demonstrate that our method can handle the challenging scenarios well. Source code is available at https://github.com/weimin581/demo_CSRNS.

Deep convolutional sparse dictionary learning for bearing fault diagnosis under variable speed condition

Dictionary learning is a usual method in the field of machinery fault diagnosis, but it requires that the rotating speed conditions of training set and test set are the same and constant. When the speed condition of test set is different from that of training set or one of them is time-vary, normal dictionary learning is difficult to get a precise sparse representation. A special dictionary model named convolutional sparse dictionary (CSD) can overcome the influence from variable speed conditions by atoms locally shifting in the sample's dimension, which is beneficial to capture the local fault features in the signal no matter how the speed changes. However, there are both large features and small features in the mechanical vibration signal, and several continuous small features can also form a large feature. The problem is that CSD can only locally optimize the signal at a fixed scale, so the features of other scales cannot be optimized. To solve this problem, this paper proposes a model named deep convolutional sparse dictionary (DCSD) to extract bearing fault features under variable speed conditions, which is improved from CSD. DCSD has multiple dictionary layers, where each layer is a CSD, but the atom's dimensions are different in each layer. The larger the number of layer is, the larger the atom's dimension is, and the sparse representation result of each layer is used to train the next dictionary layer. Through simulations cases and experimental cases under variable speed conditions, it is proved that DCSD has better performances than CSD in the fault diagnosis.

A Novel Technique for the Extraction of Dynamic Events in Extreme Ultraviolet Solar Images

High-spatial-resolution images of the solar corona acquired in the extreme ultraviolet (EUV), most notably with the Atmospheric Imaging Assembly (AIA) instrument on the Solar Dynamics Observatory (SDO) reveal the abundance of dynamic events which range from flaring bright points and jets to erupting prominences and coronal mass ejections (CMEs). In this work we present novel techniques to extract such dynamic events from the more steady background corona using 17.1 nm SDO-AIA images. The techniques presented here treat any time series of coronal images as a matrix that can be decomposed into two matrices representing the background and the dynamic component, respectively. The latter has the properties of a so-called sparse matrix, and the proposed methods are classified as methods based on sparse representations. The proposed methods are the median-filter method, the principal component pursuit, and the dynamic-mode decomposition, all of which include data pre-processing using the noise-adaptive fuzzy equalization method. The study reveals that the median-filter method and the dynamic-mode decomposition enhance all motions in the time series and produce similar results. On the other hand, the principal component pursuit enables the clear differentiation of CMEs from the background corona, thus providing a valuable tool for the characterization of their acceleration profiles in the low corona as seen in the EUV.

Regularization by double complementary priors for full waveform inversion

Full-waveform inversion (FWI) represents an advanced geophysical imaging technique focused on intricately depicting subsurface physical properties by iteratively minimizing the differences between the simulated and observed seismograms. Unfortunately, the conventional FWI utilizing a least-squares loss function suffers from various drawbacks, including the challenge of local minima and the necessity for human intervention in parameter fine-tuning. It is particularly problematic when handling noisy data and inadequate initial models. Recent works have exhibited promising performance in two-dimensional FWI by integrating structural sparse representation to procure adaptive dictionaries. Drawing inspiration from the competitiveness of structural sparse representation, we introduce a paradigm of group sparse residuals that integrates two types of complementary prior information by harnessing both the internal and external subsurface media models. The proposed algorithm is based on an alternate minimization algorithm to guarantee workflow flexibility and efficient optimization capabilities. We experimentally validate our method for two baseline geological models, and a comparison of the results demonstrates that the proposed algorithm faithfully recovers the velocity models and consistently outperforms other traditional or learning-based algorithms. A further benefit from the group sparse coding used in this method is that it reduces the sensitivity to data noise.

Improving the Ability of Measuring the Thickness of Thin Oil Slick With Ultrasound Using the Sparse Optimization Method

Improving the Ability of Measuring the Thickness of Thin Oil Slick With Ultrasound Using the Sparse Optimization Method

Super-Resolution Reconstruction of Remote Sensing Images Using Chaotic Mapping to Optimize Sparse Representation.

Current super-resolution algorithms exhibit limitations when processing noisy remote sensing images rich in surface information, as they tend to amplify noise during the recovery of high-frequency signals. To mitigate this issue, this paper presents a novel approach that incorporates the concept of compressed sensing and explores the super-resolution problem of remote sensing images for space cameras, particularly for high-speed imaging systems. The proposed algorithm employs K-singular value decomposition (K-SVD) to jointly train high- and low-resolution image blocks, updating them column by column to obtain overcomplete dictionary pairs. This approach compensates for the deficiency of fixed dictionaries in the original algorithm. In the process of dictionary updating, we innovatively integrate the circle chaotic mapping into the solution process of the dictionary sequence, replacing pseudorandom numbers. This integration facilitates balanced traversal and simplifies the search for global optimal solutions. For the optimization problem of sparse coefficients, we utilize the orthogonal matching pursuit method (OMP) instead of the L1 norm convex optimization method used in most reconstruction techniques, thereby complementing the K-SVD dictionary update algorithm. After upscaling and denoising the image using the dictionary pair mapping relationship, we further emphasize image edge details with local gradients as constraints. When compared with various representative super-resolution algorithms, our algorithm effectively filters out noise and stains in low-resolution images. It not only performs well visually but also stands out in objective evaluation indicators such as the peak signal-to-noise ratio and information entropy. The experimental results validate the effectiveness of the proposed method in super-resolution remote sensing images, yielding high-quality remote sensing image data.

Sparse representations, inference and learning

Abstract In recent years statistical physics has proven to be a valuable tool to probe into large dimensional inference problems such as the ones occurring in machine learning. Statistical physics provides analytical tools to study fundamental limitations in their solutions and proposes algorithms to solve individual instances. In these notes, based on the lectures by Marc Mézard in 2022 at the summer school in Les Houches, we will present a general framework that can be used in a large variety of problems with weak long-range interactions, including the compressed sensing problem, or the problem of learning in a perceptron. We shall see how these problems can be studied at the replica symmetric level, using developments of the cavity methods, both as a theoretical tool and as an algorithm.

Bearing fault diagnosis by sparse frequency spiral spectrum driven NAF-LDM under strong noise and small samples

Abstract The complexity of background noise and the scarcity of real fault samples seriously affect the diagnostic accuracy of the model. To address this, a noise-robust two-dimensional feature map, the sparse frequency spiral spectrum (SFSM), based on sparse representation theory, is proposed. A bridge penalty coefficient is applied to the sparse representation model to accurately select impact components, and the fast iterative shrinkage threshold algorithm is used to solve for sparse representation coefficients. Sparse reconstructed signals are obtained by convolving the impact patterns with these coefficients, leading to a sparse reconstruction algorithm with reduced computational complexity. Furthermore, the novel non-linear activation-free blocks (NAF Blocks) are embedded into the latent diffusion model to augment small samples, significantly improving image generation speed and quality. The integration of the Swin transformer for feature extraction and classification further enhances diagnostic performance. The superiority of this method is validated on the XJTU-SY dataset, a bearing experimental platform dataset, and enterprise engineering dataset. Experimental results demonstrate that the structural and generalization advantages of NAF Blocks are crucial for improving image quality and inference speed. The noise suppression capability of the proposed method, facilitated by the SFSM feature processing technique, is confirmed through ablation and noise robustness tests. Finally, the Swin transformer’s excellent feature extraction and classification capabilities for SFSM are verified. The proposed method achieves diagnostic accuracies of 99.10% and 98.7% on the XJTU-SY and experimental platform datasets, respectively.

Shrinkage estimation of gene interaction networks in single-cell RNA sequencing data

BackgroundGene interaction networks are graphs in which nodes represent genes and edges represent functional interactions between them. These interactions can be at multiple levels, for instance, gene regulation, protein-protein interaction, or metabolic pathways. To analyse gene interaction networks at a large scale, gene co-expression network analysis is often applied on high-throughput gene expression data such as RNA sequencing data. With the advance in sequencing technology, expression of genes can be measured in individual cells. Single-cell RNA sequencing (scRNAseq) provides insights of cellular development, differentiation and characteristics at the transcriptomic level. High sparsity and high-dimensional data structures pose challenges in scRNAseq data analysis.ResultsIn this study, a sparse inverse covariance matrix estimation framework for scRNAseq data is developed to capture direct functional interactions between genes. Comparative analyses highlight high performance and fast computation of Stein-type shrinkage in high-dimensional data using simulated scRNAseq data. Data transformation approaches also show improvement in performance of shrinkage methods in non-Gaussian distributed data. Zero-inflated modelling of scRNAseq data based on a negative binomial distribution enhances shrinkage performance in zero-inflated data without interference on non zero-inflated count data.ConclusionThe proposed framework broadens application of graphical model in scRNAseq analysis with flexibility in sparsity of count data resulting from dropout events, high performance, and fast computational time. Implementation of the framework is in a reproducible Snakemake workflow https://github.com/calathea24/ZINBGraphicalModel and R package ZINBStein https://github.com/calathea24/ZINBStein.

Fault diagnosis of driving gear in battery swapping system based on auditory bionics

Rack and pinion drives (RPD) are widely used in battery swapping system (BSS) for electric heavy trucks (EHT), and due to the continuous heavy-load and high-intensity operation, along with the electric erosion, the gears in the RPD are always damaged, which causes unexpected consequences such as downtime or safety incidents. The working conditions of the RPD in BSS include uncertain noises, fluctuant and low speed, which pose steep challenges to accurate fault diagnosis. Considering the auditory resistance of interference, the low-frequency sensitivity of auditory perception, and the auditory saliency mechanism, to leverage the advantages of auditory perceptual mechanism in addressing the above challenges, as the contribution in artificial intelligence, we propose an entire vibration signal processing scheme based on auditory bionics, including some mathematical models for auditory mechanisms. For the application in engineering, the proposed scheme is employed for fault diagnosis of RPD in BSS in unique working conditions. First, adaptive resampling is used to smooth the speed fluctuation, then, Gammatone filters are employed to transform vibration signals to cochleograms, after that, based on auditory stream segregation and selective attention mechanisms, effective frequency channels and salient features are extracted from the cochleograms, besides, to improve the diagnosis accuracy, binaural features are also extracted, finally, based on (sectional) sparse representation and fusion, fault diagnosis is achieved. The effectiveness of the fault diagnosis scheme is demonstrated using a BSS prototype system.