Sparse Structure Research Articles

Nonlocal Structured Sparsity Regularization Modeling for Hyperspectral Image Denoising

The non-local-based model for hyperspectral image (HSI) denoising first uses non-local self-similarity (NSS) prior to group similar full-band patches into three-dimensional non-local full-band groups (tensors) using a block matching (BM) operation, and then a low-rank (LR) penalty is typically applied to each non-local full-band group to reduce noise. While non-local-based methods have shown promising performance in HSI denoising, most existing methods have only considered the LR property of the non-local full-band group while ignoring the strong correlation between sparse coefficients. Moreover, such methods often result in unsatisfactory visual artifacts due to the noise sensitivity of BM operations, while requiring expensive computations. To address these limitations, this paper proposes a novel non-local structured sparsity regularization (NLSSR) approach for HSI denoising. First, to mitigate the noise sensitivity of the BM operation, we propose a graph-based domain distance scheme to index similar full-band patches to form the non-local full-band group. Second, we design an adaptive unidirectional low-rank (LR) dictionary with low complexity that takes into account the differences in intrinsic structure correlation among different modes of the non-local full-band tensor. Third, we utilize a global spectral LR prior to reduce spectral redundancy. Fourth, we develop a generalized soft-thresholding (GST) algorithm based on the alternating minimization framework to solve the NLSSR-based HSI denoising problem. We perform extensive experiments on both simulated and real data to show that the proposed NLSSR algorithm outperforms many popular or state-of-the-art HSI denoising methods in both quantitative and visual evaluations.

Consensus Sparsity: Multi-context Sparse Image Representation via L∞-induced Matrix Variate.

The sparsity is an attractive property that has been widely and intensively utilized in various image processing fields (e.g., robust image representation, image compression, image analysis, etc.). Its actual success owes to the exhaustive mining of the intrinsic (or homogenous) information from the whole data carrying redundant information. From the perspective of image representation, the sparsity can successfully find an underlying homogenous subspace from a collection of training data to represent a given test sample. The famous sparse representation (SR) and its variants embed the sparsity by representing the test sample using a linear combination of training samples with L0-norm regularization and L1-norm regularization. However, although these state-of-the-art methods achieve powerful and robust performances, the sparsity is not fully exploited on the image representation in the following three aspects: 1) the within-sample sparsity, 2) the between-sample sparsity, and 3) the image structural sparsity. In this paper, to make the above-mentioned multi-context sparsity properties agree and simultaneously learned in one model, we propose the concept of consensus sparsity (Con-sparsity) and correspondingly build a multi-context sparse image representation (MCSIR) framework to realize this. We theoretically prove that the consensus sparsity can be achieved by the L∞-induced matrix variate based on the Bayesian inference. Extensive experiments and comparisons with the state-of-the-art methods (including deep learning) are performed to demonstrate the promising performance and property of the proposed consensus sparsity.

Learning Nonlocal Sparse and Low-Rank Models for Image Compressive Sensing: Nonlocal sparse and low-rank modeling

The compressive sensing (CS) scheme exploits many fewer measurements than suggested by the Nyquist–Shannon sampling theorem to accurately reconstruct images, which has attracted considerable attention in the computational imaging community. While classic image CS schemes employ sparsity using analytical transforms or bases, the learning-based approaches have become increasingly popular in recent years. Such methods can effectively model the structure of image patches by optimizing their sparse representations or learning deep neural networks while preserving the known or modeled sensing process. Beyond exploiting local image properties, advanced CS schemes adopt nonlocal image modeling by extracting similar or highly correlated patches at different locations of an image to form a group to process jointly. More recent learning-based CS schemes apply nonlocal structured sparsity priors using group sparse (and related) representation (GSR) and/or low-rank (LR) modeling, which have demonstrated promising performance in various computational imaging and image processing applications.

Cross Domain Lifelong Learning Based on Task Similarity.

Humans gradually learn a sequence of cross-domain tasks and seldom experience catastrophic forgetting. In contrast, deep neural networks achieve good performance only in specific tasks within a single domain. To equip the network with lifelong learning capabilities, we propose a Cross-Domain Lifelong Learning (CDLL) framework that fully explores task similarities. Specifically, we employ a Dual Siamese Network (DSN) to learn the essential similarity features of tasks across different domains. To further understand similarity information across domains, we introduce a Domain-Invariant Feature Enhancement Module (DFEM) to better extract domain-invariant features. Moreover, we propose a Spatial Attention Network (SAN) that assigns different weights to various tasks based on the learned similarity features. Ultimately, to maximize the use of model parameters for learning new tasks, we propose a Structural Sparsity Loss (SSL) that can make the SAN as sparse as possible while ensuring accuracy. Experimental results show that our method effectively reduces catastrophic forgetting compared with state-of-the-art methods when continuously learning multiple tasks across different domains. It is worth noting that the proposed method scarcely forgets old knowledge while consistently enhancing the performance of learned tasks, more closely aligning with human learning.

Hyperspectral Compressed Sensing Reconstruction Applying Multi‐TV Collaboration

For hyperspectral images (HSI) compressed sensing reconstruction, the 3D total variation (3DTV) is a powerful regulation term encoding the spatial‐spectral local smooth prior structure. The term is calculated by supposing the sparsity structure on a gradient map along the spatial and spectral direction. In some real scenes, however, the gradient maps along different directions of HSI are not always sparse. Actually, TV constraints established on the gradient map of the original HSI are more effective in most cases. In this paper, instead of imposing sparsity on gradient maps themselves directly, compressed sensing (CS) reconstruction for HSI is formulated as an optimization problem utilizing a novel regulation term named multi‐TV (MTV), which combines the sparsity prior for the gradient map and the TV projection along with other directions of the gradient map. We also develop a workable utility algorithm based on the alternating direction method of multipliers (ADMM) to effectively deal with the optimization problem. The proposed MTV term can easily replace the conventional 3DTV term and be embedded into hyperspectral CS (HCS) reconstruction to improve its performance. Experimental results show that compared with similar state‐of‐the‐art methods, the proposed MTV term can significantly improve reconstruction precision for HCS.

Estimation of high-dimensional change-points under a group sparsity structure

Change-points are a routine feature of ‘big data’ observed in the form of high-dimensional data streams. In many such data streams, the component series possess group structures and it is natural to assume that changes only occur in a small number of all groups. We propose a new change point procedure, called groupInspect, that exploits the group sparsity structure to estimate a projection direction so as to aggregate information across the component series to successfully estimate the change-point in the mean structure of the series. We prove that the estimated projection direction is minimax optimal, up to logarithmic factors, when all group sizes are of comparable order. Moreover, our theory provide strong guarantees on the rate of convergence of the change-point location estimator. Numerical studies demonstrates the competitive performance of groupInspect in a wide range of settings and a real data example confirms the practical usefulness of our procedure.

Sparse Functional Principal Component Analysis in High Dimensions

Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller than the sample size $n$). In this work, we focus on high-dimensional functional processes where the number of random functions $p$ is comparable to, or even much larger than $n$. Such data are ubiquitous in various fields such as neuroimaging analysis, and cannot be properly modeled by existing methods. We propose a new algorithm, called sparse FPCA, which is able to model principal eigenfunctions effectively under sensible sparsity regimes. While sparsity assumptions are standard in multivariate statistics, they have not been investigated in the complex context where not only is $p$ large, but also each variable itself is an intrinsically infinite-dimensional process. The sparsity structure motivates a thresholding rule that is easy to compute without nonparametric smoothing by exploiting the relationship between univariate orthonormal basis expansions and multivariate Kahunen-Lo\`eve (K-L) representations. We investigate the theoretical properties of the resulting estimators, and illustrate the performance with simulated and real data examples.

3D Optical Sectioning Microscopy with Sparse Structured Illumination

3D Optical Sectioning Microscopy with Sparse Structured Illumination

Pattern-Coupled Baseline Correction Method for Near-Infrared Spectroscopy Multivariate Modeling

In near-infrared (NIR) modeling, the baseline drift tends to affect the qualitative and quantitative performance of the multivariate calibration model. Baseline correction method based on the sparse representation of independent wavelength is a recent method for pure spectra estimation. In fact, the measured NIR generally exhibit local wavelength coupling sparse properties, and the existing baseline correction methods suffer from performance degradation due to ignoring the wavelength coupling effect on baseline correction. In this paper, the pattern-coupled learning framework considering the local coupling property is proposed to achieve pure spectrum fitting and baseline correction simultaneously. Specifically, the pattern-coupled hierarchical Gaussian prior model is introduced to characterize the local sparse structure corresponding to characteristic peaks with wavelength coupling. The adaptive coupling method is further proposed to achieve robust learning of NIR under different noise interference. Unlike conventional frameworks where wavelength or hyperparameters are learned independently, the proposed mode coupling framework enables accurate baseline estimation without prior knowledge of spectral structure by characterizing wavelength coupling properties. Compared with the state-of-the-art methods, the RMSE and R2 of the proposed method are reduced and increased by 14.41% and 1.53%, 14.12% and 2.01%, 12.86% and 12.93% in three measured NIR datasets, respectively.

ИССЛЕДОВАНИЕ ХАРАКТЕРИСТИК РАЗВЕРТЫВАЕМОЙ КОСМИЧЕСКОЙ ЗЕРКАЛЬНОЙ АНТЕННЫ С РАЗРЕЖЕННОЙ ОТРАЖАЮЩЕЙ ПОВЕРХНОСТЬЮ

The article presents the results of a study of the characteristics of a space parabolic mirror with a deployable reflector. A model of the reflector truss structure formed by two asymmetric parabolic networks with tension cables is presented. Three variants of the sparse structure of the reflecting film of the reflector are presented, differing in periodically repeating hexagonal holes with different sizes. A complex electrodynamic modeling of the radiation characteristics of a parabolic mirror antenna with a developed model of a truss-bearing structure and the proposed structures of reflective films, allowing to reduce the mass of the reflector and increase the reliability of the antenna system, are carried out. The estimation of the frequency dependences of the characteristics of the variants of the parabolic mirror antenna model is given. Recommendations on the use of sparse reflective films for small, medium and large apertures of deployable reflectors are proposed.

Cglasso: An R Package for Conditional Graphical Lasso Inference with Censored and Missing Values

Sparse graphical models have revolutionized multivariate inference. With the advent of high-dimensional multivariate data in many applied fields, these methods are able to detect a much lower-dimensional structure, often represented via a sparse conditional independence graph. There have been numerous extensions of such methods in the past decade. Many practical applications have additional covariates or suffer from missing or censored data. Despite the development of these extensions of sparse inference methods for graphical models, there have been so far no implementations for, e.g., conditional graphical models. Here we present the general-purpose package cglasso for estimating sparse conditional Gaussian graphical models with potentially missing or censored data. The method employs an efficient expectation-maximization estimation of an ℓ₁ -penalized likelihood via a block-coordinate descent algorithm. The package has a user-friendly data manipulation interface. It estimates a solution path and includes various automatic selection algorithms for the two ℓ₁ tuning parameters, associated with the sparse precision matrix and sparse regression coefficients, respectively. The package pays particular attention to the visualization of the results, both by means of marginal tables and figures, and of the inferred conditional independence graphs. This package provides a unique and computational efficient implementation of a conditional Gaussian graphical model that is able to deal with the additional complications of missing and censored data. As such it constitutes an important contribution for empirical scientists wishing to detect sparse structures in high-dimensional data.

Multi-Target Regression Based on Multi-Layer Sparse Structure and Its Application in Warships Scheduled Maintenance Cost Prediction

The scheduled maintenance cost of warships is the essential prerequisite and economic foundation to guarantee the effective implementation of maintenance, which directly influences the quality and efficiency of maintenance operations. This paper proposes a multi-target regression algorithm based on multi-layer sparse structure (MTR-MLS) algorithm, to achieve simultaneous prediction of the subentry costs of warship scheduled maintenance, and the total cost of the maintenance is estimated by summing the predicted values of the different subentry costs. In MTR-MLS, the kernel technique is employed to map the inputs to the higher dimensional space for decoupling the complex input–output nonlinear relationships. By deploying the structure matrix, MTR-MLS achieves a latent variable model which can explicitly encode the inter-target correlations via l2,1-norm-based sparse learning. Meanwhile, the noises are encoded to diminish the influence of noises while exploiting the correlations among targets. An alternating optimization algorithm is proposed to solve the objective function. Extensive experimental evaluation on real-world datasets and datasets of warships scheduled maintenance cost show that the proposed method consistently outperforms the state-of-the-art algorithms, which demonstrates its great effectiveness for cost prediction of warships scheduled maintenance.

Exploiting Constant Trace Property in Large-scale Polynomial Optimization

We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result, such moment relaxations can be solved efficiently by first-order methods that exploit CTP, e.g., the conditional gradient-based augmented Lagrangian method. We also extend this CTP-exploiting framework to large-scale POPs with different sparsity structures. The efficiency and scalability of our framework are illustrated on some moment relaxations for various randomly generated POPs, especially second-order moment relaxations for quadratically constrained quadratic programs.

Interpreting tree ensemble machine learning models with endoR.

Tree ensemble machine learning models are increasingly used in microbiome science as they are compatible with the compositional, high-dimensional, and sparse structure of sequence-based microbiome data. While such models are often good at predicting phenotypes based on microbiome data, they only yield limited insights into how microbial taxa may be associated. We developed endoR, a method to interpret tree ensemble models. First, endoR simplifies the fitted model into a decision ensemble. Then, it extracts information on the importance of individual features and their pairwise interactions, displaying them as an interpretable network. Both the endoR network and importance scores provide insights into how features, and interactions between them, contribute to the predictive performance of the fitted model. Adjustable regularization and bootstrapping help reduce the complexity and ensure that only essential parts of the model are retained. We assessed endoR on both simulated and real metagenomic data. We found endoR to have comparable accuracy to other common approaches while easing and enhancing model interpretation. Using endoR, we also confirmed published results on gut microbiome differences between cirrhotic and healthy individuals. Finally, we utilized endoR to explore associations between human gut methanogens and microbiome components. Indeed, these hydrogen consumers are expected to interact with fermenting bacteria in a complex syntrophic network. Specifically, we analyzed a global metagenome dataset of 2203 individuals and confirmed the previously reported association between Methanobacteriaceae and Christensenellales. Additionally, we observed that Methanobacteriaceae are associated with a network of hydrogen-producing bacteria. Our method accurately captures how tree ensembles use features and interactions between them to predict a response. As demonstrated by our applications, the resultant visualizations and summary outputs facilitate model interpretation and enable the generation of novel hypotheses about complex systems.

First validation of GEDI canopy heights in African savannas

Savannas have complex, discontinuous woody vegetation structures that vary greatly in vertical and spatial arrangement and change due to climatic, ecological and management impacts. While airborne laser scanning (ALS) data have provided detailed information on vertical vegetation structure and is widely used in ecological studies, it is lacking in availability and repeat frequency. Although the Global Ecosystem Dynamics Investigation (GEDI) waveform Light Detection and Ranging (LiDAR) sensor and algorithms were optimized for measuring dense forests, it was anticipated that GEDI metrics could provide useful characterization of lower stature, sparse savannas structures. This study provided the first baseline validation of Version 2 GEDI (L2A) relative height 98 (RH98) by comparing the on-orbit GEDI-RH98orb to the simulated GEDI-RH98sim derived from ALS data across diverse savanna vegetation. It furthermore determined the influence of various factors on error, e.g. algorithm setting group (SGs), beam type, day vs. night, beam sensitivity, and vegetation phenology. After applying quality flags, 22,813 GEDI footprints were analyzed across 11 sites. SGs 4–6 that are aimed at dense forests had much larger errors than SGs 1–3. The phenological conditions at the time of GEDI data acquisition had a very large influence on the error of RH98orb. During leaf-on conditions for savanna vegetation with RH98sim < 15 m, RH98orb was very accurate with R2 = 0.61, mean bias = −0.55 m, %bias = −11.1%, RMSE = 1.64 m and %RMSE = 29.8%. In leaf-off conditions where RH98sim < 15 m, RH98orb was less accurate with R2 = 0.43, mean bias = −1.47 m, %bias = −26.5%, RMSE = 2.03 m and %RMSE = 40.9%. During leaf-off conditions, the GEDI LiDAR signal at the start of the waveform may be weaker as it interacts with denuded branches and may be truncated as noise, leading to a large negative height bias. Therefore, assessments of deciduous vegetation structures should be conducted during leaf-on periods. In leaf-on conditions, GEDI's RH98orb was very accurate between canopy heights of 3 and 7 m, with a mean bias of −0.79 m (−10%). The bias of RH98orb was not influenced by canopy cover. Due to the GEDI LiDAR pulse width of 15.6 ns, the GEDI-RH98 data product cannot reliably estimate canopy heights of shrubs below 2.34 m and will require more complex deconvolution of the waveform. GEDI's RH98 accurately estimates the canopy height of trees between 3 and 15 m allowing assessment of canopy heights over vast savanna areas.

Long short‐distance topology modelling of 3D point cloud segmentation with a graph convolution neural network

Abstract3D point cloud segmentation is a non‐trivial problem due to its irregular, sparse, and unordered data structure. Existing methods only consider structural relationships of a 3D point and its spatial neighbours. However, the inner‐point interactions and long‐distance context of a 3D point cloud have been less investigated. In this study, we propose an effective plug‐and‐play module called the Long Short‐Distance Topologically Modelled (LSDTM) Graph Convolutional Neural Network (GCNN) to learn the underlying structure of 3D point clouds. Specifically, we introduce the concept of subgraph to model the contextual‐point relationships within a short distance. Then the proposed topology can be reconstructed by recursive aggregation of subgraphs, and importantly, to propagate the contextual scope to a long range. The proposed LSDTM can parse the point cloud data with maximisation of preserving the geometric structure and contextual structure, and the topological graph can be trained end‐to‐end through a seamlessly integrated GCNN. We provide a case study of triple‐layer ternary topology and experimental results on ShapeNetPart, Stanford 3D Indoor Semantics and ScanNet datasets, indicating a significant improvement on the task of 3D point cloud segmentation and validating the effectiveness of our research.

Scaphium scaphigerum/graphene hybrid aerogel for composite phase change material with high phase change enthalpy and high thermal conductivity for energy storage

Based on the disadvantages of the low thermal conductivity and easy leakage of the organic phase change energy storage material, Scaphium scaphigerum/graphene hybrid aerogel (SGA) with sparse porous structure was prepared by the template method and used as a thermally conductive reinforcing material to fabricate PEG forming composite PCMs of SGA/PEG. The results show that the three-dimensional pore structure of the SGA is composed of extremely thin graphene sheets interwoven and connected to each other. The EDA reducing agent can effectively remove the oxygen-containing functional groups, allowing the graphene sheets to re-adhere to the SC soft stencil and continuously aggregate, stack and self-assemble, resulting in thermally stable SGA. DSC result shows SGA/PEG composite has excellent overall thermal performance, especially SGA/PEG-8 with a latent thermal storage energy of 166.11 J/g, which is 99.35 % of that of pure PEG, and remains 99.20 % even after 100 heating-cooling cycles. The XRD, FT-IR and Raman spectroscopy results show that there is no chemical reaction in the SGA composite with PEG and that it is physically bonded. The TGA results show that the SGA can effectively conduct heat from the surface of the sample, showing a beneficial effect on the thermal stability of the composite. The SEM results directly demonstrate that the three-dimensional pore structure of the SGA is uniformly wrapped by PEG and that the surface of the lamellae is relatively smooth, without any significant accumulation of PEG. Furthermore, the shape-stable SGA/PEG exhibited a high thermal conductivity of 1.0621 W/(m K) which was enhanced to 378 % relative to pure PEG. This novel strategy offers enlightening prospects for the preparation of composite phase change materials with good thermal storage properties, thermal conductivity and thermal stability for a wide range of applications in energy storage.

The mechanism study of laser peeling of ultra-thin polyimide film from the transparent substrate

Laser peeling of ultra-thin polyimide (PI) film from transparent substrate is a critical technology in the flexible electronics industry. This paper studies the laser ablation and interface separation of the PI film to reveal the mechanism of laser peeling. In the laser ablation process, the supercritical environment is formed, and gas bubbles appear. Then the gas bubbles fuse together and become cavitation holes. These cavitation holes fuse together and produce sparse nanopillar structures that can be seen as a blister. In the interface separation process, the blister absorbs thermal energy and expands under laser irradiation. This paper proposes a discrete quasi-static method to analyze the separation of the PI film from the transparent substrate during the blister expansion. The cohesive zone model is also introduced to predict the peeling behaviors of the PI film. The results show that the blister profile is related to the laser influence, and the blister profile obtained by the theoretical model can fit well with the experiment. When the laser fluence is larger, the blister profile is steeper, and the pressure inside the blister is larger. This paper provides a new perspective for understanding the laser peeling mechanism of ultra-thin PI film from a transparent substrate.

Joint spatial structural sparsity constraint and spectral low-rank approximation for snapshot compressive spectral imaging reconstruction

Snapshot compressive spectral imaging (SCI) is a potential technology in the field of hyperspectral imaging (HSI), where multi-frame spectral images are compressed into a single snapshot measurement and collected by a 2D detector. Existing reconstruction algorithms of SCI systems do not make full use of the redundancy of hyperspectral data, artifacts and blur degrade the quality of the reconstruction target image. In this paper, an efficient algorithm, named as spatial structural sparsity and spectral low-rank priors (SSS-SLR), is proposed based on two inherent priors of hyperspectral images. Specifically, the spatial structural sparsity and spectral low-rank priori are simultaneously integrated into the SCI image restoration process to establish a variational optimization model, which can be solved via an alternating minimization algorithm. Extensive reconstruction results of hyperspectral data cube from both synthetic and real datasets demonstrate that the proposed method significantly outperforms the canonical algorithms.

An enhanced beamspace channel estimation algorithm for wideband millimeter-wave massive MIMO systems

Accurate beamspace channel estimation is critical in wideband millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) communication systems. However, the beam squint effect caused by the increase in bandwidth and array dimension can bring additional challenges to the wideband channel estimation. In this study, we propose a wideband channel estimation scheme based on compressed sensing to solve the beam squint effect in broadband mmWave massive MIMO systems. First, the channel estimation problem is transformed into a beamspace direction estimation problem by exploiting the special frequency-dependent sparse structure of a broadband beamspace channel. Then, we propose a beam-band function-based orthogonal matching pursuit algorithm, in which a beam-band function is constructed and used to capture the power of each path component to estimate the spatial direction. In addition, the support of each path component at different sub-carriers is estimated to reduce the influence of the beam squint effect. Moreover, the support is estimated adaptively to improve the estimation accuracy further. Simulation results demonstrate that the proposed scheme reduces the pilot overhead under the beam squint effect and improve the estimation accuracy significantly.