Sparse Ones Research Articles

Accelerating multipool CEST MRI of Parkinson's disease using deep learning-based Z-spectral compressed sensing.

To develop a deep learning-based approach to reduce the scan time of multipool CEST MRI for Parkinson's disease (PD) while maintaining sufficient prediction accuracy. A deep learning approach based on a modified one-dimensional U-Net, termed Z-spectral compressed sensing (CS), was proposed to recover dense Z-spectra from sparse ones. The neural network was trained using simulated Z-spectra generated by the Bloch equation with various parameter settings. Its feasibility and effectiveness were validated through numerical simulations and in vivo rat brain experiments, compared with commonly used linear, pchip, and Lorentzian interpolation methods. The proposed method was applied to detect metabolism-related changes in the 6-hydroxydopamine PD model with multipool CEST MRI, including APT, CEST@2 ppm, nuclear Overhauser enhancement, direct saturation, and magnetization transfer, and the prediction performance was evaluated by area under the curve. The numerical simulations and in vivo rat-brain experiments demonstrated that the proposed method could yield superior fidelity in retrieving dense Z-spectra compared with existing methods. Significant differences were observed in APT, CEST@2 ppm, nuclear Overhauser enhancement, and direct saturation between the striatum regions of wild-type and PD models, whereas magnetization transfer exhibited no significant difference. Receiver operating characteristic analysis demonstrated that multipool CEST achieved better predictive performance compared with individual pools. Combined with Z-spectral CS, the scan time of multipool CEST MRI can be reduced to 33% without distinctly compromising prediction accuracy. The integration of Z-spectral CS with multipool CEST MRI can enhance the prediction accuracy of PD and maintain the scan time within a reasonable range.

Approximate GCD of several multivariate sparse polynomials based on SLRA interpolation

To compute the greatest common divisor (GCD) of a set of multivariate polynomials, modular algorithms are typically employed to prevent any growth in the coefficient polynomials in the intermediate expressions. However, when dealing with multivariate polynomials with a priori errors on their coefficients, using such modular algorithms becomes challenging. This is because any resulting approximate GCD computed in one variable may have perturbations depending on the evaluation point and may not be an image of the same desired multivariate approximate GCD. This necessitates computing it as given multivariate polynomials, and operating with large matrices whose size is exponential in the number of variables. In this paper, we present a new modular algorithm, suitable for dense cases and effective for sparse ones, called “SLRA interpolation”. This algorithm uses the multidimensional fast Fourier transform (FFT) and the structured low-rank approximation (SLRA) of non-square block diagonal matrices. The SLRA interpolation technique may reduce the time-complexity for one iteration in the computation of approximate GCD of several multivariate polynomials, especially for the sparse case.

Learnable differencing center for nighttime depth perception

Depth completion is the task of recovering dense depth map from sparse ones, usually with the help of color images. Existing image guided methods perform well on daytime depth perception self-driving benchmarks, but struggle in nighttime scenarios with poor visibility and complex illumination. To address these challenges, we propose a simple yet effective learnable differencing center network (LDCNet). The key idea is to use recurrent inter-convolution differencing (RICD) and illumination affinitive intra-convolution differencing (IAICD) to enhance the nighttime color images and reduce the negative effects of the varying illumination, respectively. RICD explicitly estimates global illumination by differencing two convolutions with different kernels, treating the small-kernel-convolution feature as the center of the large-kernel-convolution feature in a new perspective. IAICD softly alleviates the local relative light intensity by differencing a single convolution, where the center is dynamically aggregated based on neighboring pixels and the estimated illumination map in the RICD. On both nighttime depth completion and depth estimation tasks, extensive experiments demonstrate the effectiveness of our LDCNet, reaching the state of the art.

RANSAC-Based Planar Point Cloud Segmentation Enhanced by Normal Vector and Maximum Principal Curvature Clustering

Abstract. Planar feature segmentation is an essential task for 3D point cloud processing, finding many applications in various fields such as robotics and computer vision. The Random Sample Consensus (RANSAC) is one of the most common algorithms for the segmentation, but its performance, as given by the original form, is usually limited due to the use of a single threshold and interruption of similar planar features presented close to each other. To address these issues, we present a novel point cloud processing workflow which aims at developing an initial segmentation stage before the basic RANSAC is performed. Initially, normal vectors and maximum principal curvatures for each point of a given point cloud are analyzed and integrated. Subsequently, a subset of normal vectors and curvature is utilized to cluster planes with similar geometry based on the region growing algorithm, serving as a coarse but fast segmentation process. The segmentation is therefore refined with the RANSAC algorithm which can be now performed with higher accuracy and speed due to the reduced interference. After the RANSAC process is applied, resultant planar point clouds are built from the sparse ones via a point aggregation process based on geometric constraints. Four datasets (three real and one simulated) were used to verify the method. Compared to the classic segmentation method, our method achieves higher accuracy, with an RMSE from fitting equal to 0.0521 m, along with a higher recall of 93.31% and a higher F1-score of 95.38%.

LDDMM-Face: Large deformation diffeomorphic metric learning for cross-annotation face alignment

We propose an innovative, flexible, and consistent cross-annotation face alignment framework, LDDMM-Face, the key contribution of which is a deformation layer that naturally embeds facial geometry in a diffeomorphic way. This enables and solves cross-annotation face alignment tasks that were impossible in the existing works. Instead of predicting facial landmarks via a heatmap or coordinate regression, we formulate the face alignment task in a diffeomorphic registration manner and predict momenta that uniquely parameterize the deformation between the initial boundary and true boundary. We then perform large deformation diffeomorphic metric mapping (LDDMM) simultaneously for curve and landmark to localize the facial landmarks. The novel embedding of LDDMM into a deep network allows LDDMM-Face to consistently annotate facial landmarks without ambiguity and flexibly handle various annotation schemes, and can even predict dense annotations from sparse ones. To the best of our knowledge, this is the first study to leverage learning-based diffeomorphic mapping for face alignment. Our method can be easily integrated into various face alignment networks. We extensively evaluate LDDMM-Face on five benchmark datasets: 300W, WFLW, HELEN, COFW-68, and AFLW. LDDMM-Face distinguishes itself with outstanding performance when dealing with within-dataset cross-annotation learning (sparse-to-dense) and cross-dataset learning (different training and testing datasets). In addition, LDDMM-Face shows promising results on the most challenging task of cross-dataset cross-annotation learning (different training and testing datasets with different annotations). Our codes are available at https://github.com/CRazorback/LDDMM-Face.

CSRNet: Focusing on critical points for depth completion

Depth completion is an effective method for generating dense depth maps from sparse ones. In recent studies, the majority of points, which we call standard points, often exhibit sub-optimal performance. This issue arises from the need to fit only very few points, termed as challenging points, which consist of noises and regions with discontinuous depth in the ground-truth. On the other hand, traditional evaluations can not recognize this situation, and are dominated by these limited challenging points, whose performance improvements may not significantly benefit related tasks. In contrast, standard points, which are critical for these tasks, are not effectively measured. This discrepancy highlights the need for a more targeted approach and evaluation method for depth completion. In order to solve the above problems, we propose a standard-point-enhancing learning paradigm. This paradigm aims to improve the performance on standard points, which consists of a Cascaded Segmentation-to-Regression Networks (CSRNet) and a Mining L1 loss. CSRNet includes two branches: DSNet and DRNet. DSNet uses segmentation to generate a coarse depth map, providing challenging-point-insensitive information. DRNet adopts a coarse-to-fine approach to learn the residual depth map between the coarse depth map and the ground-truth depth map. In addition, our Mining L1 loss leverages the segmentation results to filter out potential challenging points. This approach allows the network to concentrate more effectively on standard points. Lastly, we introduce the Minimum Error (ME) Curves as a new way to measure the performance of predicted depth maps in a flexible and comprehensive manner, irrespective of whether the points are standard or challenging. Experimental results on the KITTI and NYUDv2 datasets show that our approach significantly improves accuracy on the majority of points.

Circuit complexity of quantum access models for encoding classical data

How to efficiently encode classical data is a fundamental task in quantum computing. While many existing works treat classical data encoding as a black box in oracle-based quantum algorithms, their explicit constructions are crucial for the efficiency of practical algorithm implementations. Here, we unveil the mystery of the classical data encoding black box and study the Clifford + T complexity in constructing several typical quantum access models. For general matrices (even including sparse ones), we prove that sparse-access input models and block-encoding both require nearly linear circuit complexities relative to the matrix dimension. We also give construction protocols achieving near-optimal gate complexities. On the other hand, the construction becomes efficient with respect to the data qubit when the matrix is a linear combination of polynomial terms of efficiently implementable unitaries. As a typical example, we propose improved block-encoding when these unitaries are Pauli strings. Our protocols are built upon improved quantum state preparation and a select oracle for Pauli strings, which hold independent values. Our access model constructions provide considerable flexibility, allowing for tunable ancillary qubit numbers and offering corresponding space-time trade-offs.

Efficient Learning of PDEs via Taylor Expansion and Sparse Decomposition into Value and Fourier Domains

Accelerating the learning of Partial Differential Equations (PDEs) from experimental data will speed up the pace of scientific discovery. Previous randomized algorithms exploit sparsity in PDE updates for acceleration. However such methods are applicable to a limited class of decomposable PDEs, which have sparse features in the value domain. We propose Reel, which accelerates the learning of PDEs via random projection and has much broader applicability. Reel exploits the sparsity by decomposing dense updates into sparse ones in both the value and frequency domains. This decomposition enables efficient learning when the source of the updates consists of gradually changing terms across large areas (sparse in the frequency domain) in addition to a few rapid updates concentrated in a small set of “interfacial” regions (sparse in the value domain). Random projection is then applied to compress the sparse signals for learning. To expand the model applicability, Taylor series expansion is used in Reel to approximate the nonlinear PDE updates with polynomials in the decomposable form. Theoretically, we derive a constant factor approximation between the projected loss function and the original one with poly-logarithmic number of projected dimensions. Experimentally, we provide empirical evidence that our proposed Reel can lead to faster learning of PDE models (70-98% reduction in training time when the data is compressed to 1% of its original size) with comparable quality as the non-compressed models.

PU-Flow: a Point Cloud Upsampling Network with Normalizing Flows.

Point cloud upsampling aims to generate dense point clouds from given sparse ones, which is a challenging task due to the irregular and unordered nature of point sets. To address this issue, we present a novel deep learning-based model, called PU-Flow, which incorporates normalizing flows and weight prediction techniques to produce dense points uniformly distributed on the underlying surface. Specifically, we exploit the invertible characteristics of normalizing flows to transform points between Euclidean and latent spaces and formulate the upsampling process as ensemble of neighbouring points in a latent space, where the ensemble weights are adaptively learned from local geometric context. Extensive experiments show that our method is competitive and, in most test cases, it outperforms state-of-the-art methods in terms of reconstruction quality, proximity-to-surface accuracy, and computation efficiency. The source code will be publicly available at https://github.com/unknownue/puflow.

Functional Matrices on Quantum Computing Simulation

In simulating Quantum Computing by using the circuit model the size of the matrices to deal with, together with the number of products and additions required to apply every quantum gate becomes a really hard computational restriction. This paper presents a data structure, called Functional Matrices, which is the most representative feature of QSimov quantum computing simulator which is also provided and tested. A comparative study of the performance of Functional Matrices with respect to the other two most commonly used matrix data structures, dense and sparse ones, is also performed and summarized within this work.

A robust sparse Bayesian learning method for the structural damage identification by a mixture of Gaussians

Sparse Bayesian learning methods have been successfully applied to the community of structural damage identification, which commonly assumes that the uncertainties from modeling errors and measurement noises follow Gaussian distribution. However, this assumption typically compromises the accuracy of damage identification because these real uncertainties may not follow a Gaussian distribution. A mixture of Gaussian distributions can more accurately quantify the real uncertainties of damage identification than a Gaussian distribution because it can theoretically approximate any continuous distribution. Motivated by this, we utilized a robust sparse Bayesian learning method to investigate the problem of structural damage identification and further improve the accuracy of damage identification. This method includes a sparse Bayesian learning model with a mixture of Gaussians and an expectation–maximization algorithm based on the Laplace approximation technique. The numerical and experimental results illustrate that our method improves the damage identification accuracy by 6.78% and 11.92% than the existing two sparse Bayesian learning ones, respectively.

WBEM-based analysis of band structures of solid-solid and fluid-fluid phononic crystals with frequency-independent fundamental solutions

A novel method is presented to determine the band structures of two-dimensional solid-solid and fluid-fluid phononic crystals (PCs) with square and triangular lattices using the wavelet-based boundary element method (WBEM). Both sweeping frequency technique and sweeping wave vector technique are used to determine the band structures of PCs. The fundamental solutions for integral equations established in primitive cell are independent of angular frequency, resulting in an avoidance of solving nonlinear eigenvalue problems and much reduction of computing time. The radial integration method and dual reciprocity method are respectively applied to handle the domain integral terms arising from the use of frequency-independent fundamental solutions, and to make the dimension reduction. The physical fields are approximated by B-spline wavelet on the interval and wavelet coefficients in wavelet space. It is proved that the wavelet coefficients still meet the relationship of their corresponding physical quantities, such as Bloch theorem. By means of the vanishing moment characteristic of wavelets, some small entries are produced in the system matrices which are further compressed into sparse ones, and the influence of sparse matrices on the results is discussed. Finally, the high computing speed and accuracy of the proposed method are shown in examples.

Projected Generative Adversarial Network for Point Cloud Completion

Acquiring semantics directly from a point cloud is an important requirement for handling point cloud tasks. However, point clouds captured with laser scanner equipment are often incomplete due to the limitations posed by target occlusion and light reflection. Consequently, recovering the complete point clouds from partial and sparse ones is essential for further studies. In this paper, we model a novel projected generative adversarial network (PGAN) for point cloud completion. First, we present a multi-scale generator module (MSGM) to fully capture the local structures and global shape in the raw incompletion point cloud and generate the multi-scale complete point cloud. In contrast to existing point cloud feature extractors, our MSGM promotes a correlation between different regions of an incomplete point cloud and integrates the contextual information of the point cloud. Second, we observe that the existing point discriminator is inadequate to enhance the discrimination of the prediction point cloud. To address this problem, we project the completed point cloud to 2D maps and apply adversarial training to discriminate the geometrical shape from a specific viewpoint. Comprehensive experiments on the ShapeNet and ModelNet40 datasets show that the proposed method performs well against existing point cloud completion tasks. We also present an ablation study to demonstrate the advantages of the projected generative adversarial network.

Minor embedding with Stuart-Landau oscillator networks

We theoretically implement a strategy from quantum computation architectures to simulate Stuart-Landau oscillator dynamics in all-to-all connected networks, also referred to as complete graphs. The technique builds upon the triad structure minor embedding which expands dense graphs of interconnected elements into sparse ones which can potentially be realized in future on-chip solid-state technologies with tunable edge weights. As a case study, we reveal that the minor embedding procedure allows simulating the XY model on complete graphs, thus bypassing a severe geometric constraint.

A test for the identity of a high-dimensional correlation matrix based on the [formula omitted]-norm

This paper presents a new test procedure for the identity of a correlation matrix in high-dimensional asymptotic frameworks, the statistic of which is based on the ℓ4-norm of off-diagonal entries of the covariance matrix. A striking finding is that this test can achieve full power against both dense alternatives and sparse ones. Simulation results demonstrate its superiority over some competitors in various cases.

Consensual Regression of Lasso-Sparse PLS models for Near-Infrared Spectra of Food

In some cases, near-infrared spectra (NIRS) make the prediction of quantitative models unreliable, and the choice of a suitable number of latent variables (LVs) for partial least square (PLS) is difficult. In this case, a strategy of fusing member models with important information is gradually becoming valued in recent research. In this work, a series of PLS regression models were developed with an increasing number of LVs as member models. Then, the least absolute shrinkage and selection operator (Lasso) was employed as the model’s selection access to sparse uninformative ones among these PLS member models. Deviation weighted fusion (DW-F), partial least squares regression coefficient fusion (PLS-F), and ridge regression coefficient fusion (RR-F) were comparatively used further to fuse the above sparsed member models, respectively. Three spectral datasets, including six attributes in NIR data of corn, apple, and marzipan, respectively, were applied in order to validate the feasibility of this fusion algorithm. Six fusion models of the above attributes performed better than the general optimal PLS model, with a noticeable enhancement of root mean errors squared of prediction (RMSEP) arriving at its highest at 80%. It also reduced more than half of the spectral bands; the DW-F especially showed its excellent fusing capacity and obtained the best performance. Results show that the preferred strategy of DW-F model combined with Lasso selection can make full use of spectral information, and significantly improve the prediction accuracy of fusion models.

Convolutional Neural Networks and Heuristic Methods for Crowd Counting: A Systematic Review.

The crowd counting task has become a pillar for crowd control as it provides information concerning the number of people in a scene. It is helpful in many scenarios such as video surveillance, public safety, and future event planning. To solve such tasks, researchers have proposed different solutions. In the beginning, researchers went with more traditional solutions, while recently the focus is on deep learning methods and, more specifically, on Convolutional Neural Networks (CNNs), because of their efficiency. This review explores these methods by focusing on their key differences, advantages, and disadvantages. We have systematically analyzed algorithms and works based on the different models suggested and the problems they are trying to solve. The main focus is on the shift made in the history of crowd counting methods, moving from the heuristic models to CNN models by identifying each category and discussing its different methods and architectures. After a deep study of the literature on crowd counting, the survey partitions current datasets into sparse and crowded ones. It discusses the reviewed methods by comparing their results on the different datasets. The findings suggest that the heuristic models could be even more effective than the CNN models in sparse scenarios.

Spatially Driven Chemical Species Tomography With Size-Adaptive Hybrid Meshing Scheme

This paper develops a size-adaptive hybrid meshing scheme for Chemical Species Tomography (CST) that is driven by the customized spatial resolution of the sensing region. Traditionally, the entire sensing region in CST is uniformly discretized with the empirically determined density of the meshes. Such a discretization results in a) waste of computational efforts on the less spatially resolved location; and b) much severer rank deficiency. To solve the above-mentioned issues, we introduce, for the first time, a size-adaptive hybrid meshing scheme for CST. Driven by the spatial resolution, dense meshes are deployed in the region of interest (RoI) to detail the target flow field while sparse ones are deployed out of the RoI to fully consider the physically existing laser absorption. The proposed scheme is numerically validated using a CST sensor with 128 laser beams. The visual and quantitative metric comparisons show that the proposed hybrid-size meshing scheme outperforms the traditionally uniform-size meshing scheme, giving 35% lower image error and 38% less significant dislocation at a typical 35 dB signal-to-noise ratio in the RoI. The proposed hybrid-size meshing scheme significantly facilitates the reconstruction of the industrial combustion processes where the combustion zone is bypassed by cooling flows. In these scenarios, the proposed scheme can adapt a finer resolution to detail the combustion zone, while maintaining the integrity of the physical model by less resolved reconstruction of the bypass flows.

A generative node-attribute network model for detecting generalized structure and semantics

A challenge of community detection in attributed networks is how we can design an effective and efficient clustering method that can not only discover a wide of structure types but also have good community semantic annotations. To this end, by sharing the latent position of nodes, a mathematically principled model (named GNAN) that fuses topological information and node-attribute information is developed. Using the expectation–maximization algorithm, the latent position of each node and the model parameters are learned. The new model detects communities more accurately than can be done with topology information alone. And a case study is provided to show the ability of our model in the semantic interpretability of communities. In detail, firstly, inspired by the idea of NMM (Newman’s Mixture Models), a group of parameters that characterize the link behaviors of nodes is introduced into the topological model. In the probabilistic sense, nodes with the same link pattern form a community. Therefore, the combined model can generate not only traditional communities, i.e., groupings of nodes with dense internal connections and sparse external ones, but also a range of other types of structure in networks, such as bipartite structure, core–periphery structure, and their mixture structure, which are collectively referred to as generalized structure. Secondly, based on the homogeneity assumption, another group of parameters describing the distribution of attributes in a community is introduced into the attributed model. Under the control of these parameters, the united model can generate different attributes according to the probability, and automatically discover the critical attributes of the community. Finally, experiments on both synthetic and real-world networks with various network structures show that the new model can detect communities more accurately than the related state-of-the-art models.

Sparse deconvolution methods for online energy estimation in calorimeters operating in high luminosity conditions

Energy reconstruction in calorimeters operating in high luminosity particle colliders has become a remarkable challenge. In this scenario, pulses from a calorimeter front-end output overlap each other (pile-up effect), compromising the energy estimation procedure when no preprocessing for signal disentanglement is accomplished. Recently, methods based on signal deconvolution have been proposed for both online and offline reconstructions. For online processing, constraints concerning fast processing, memory requirements, and cost implementation limit the overall performance. Offline reconstruction allows the use of Sparse Representation theory to implement sophisticated Iterative Deconvolution methods. This paper presents Iterative Deconvolution methods based on Sparse Representation algorithms whose computational cost is effective for online implementation. Using simulated data, current techniques were compared to the proposed Sparse Representation ones for performance validation in the online environments. Analysis has shown that, despite the higher computational cost, when compared to standard methods, the performance improvement may justify the use of the proposed techniques, in particular for the Separable Surrogate Functional, which is shown to be feasible for implementation in modern FPGAs.