Minimum Norm Research Articles

Resting state connectivity biomarkers of seizure freedom after epilepsy surgery

Alterations in brain networks may cause the lowering of the seizure threshold and hypersynchronization that underlie the recurrence of unprovoked seizures in epilepsy. The aim of this work is to estimate functional network characteristics, which may help predicting outcome of epilepsy surgery.Twenty patients were studied (11 females, 9 males, mean age 33 years) with scalp-recorded HD-EEG in resting state (eyes closed, no interictal discharges) before intracranial evaluation, which allowed the precise determination of the epileptogenic zone. Dipole source time courses in the brain were estimated using Weighted Minimum Norm Estimate based on HD-EEG signals. Information inflow and outflow of atlas-based brain regions were computed using partial directed connectivity. A set of graph measures for pairwise connections in standard EEG frequency bands was calculated.After epilepsy surgery 10 patients were seizure-free (Engel 1a) and 10 patients continued suffering from seizures (Engel outcome worse than 1a). Inflow of the regions containing the epileptogenic zone in the beta and delta frequency bands was significantly lower in patients who achieved seizure-freedom after surgery, compared with patients who continued to have seizures (p = 0.012, and p = 0.026, respectively). Average path length in the beta frequency band was significantly higher in patients who achieved seizure freedom (p = 0.012). In the delta frequency band, local efficiency and clustering coefficient were significantly higher in patients who achieved seizure freedom (0.033, 0.046).In patients who achieved seizure freedom after surgery, the preoperative analysis of the epileptic network exhibited stronger separation of the region containing the seizure onset zone, with less inflow of information. In contrast, shorter paths within the epileptic network may facilitate hypersynchronous neuronal activity and thus the recurrence of seizures in non-seizure free patients. This study supports the hypothesis that epileptic network properties might help to define suitable candidates for epilepsy surgery.

Effect of Inverse Solutions, Connectivity Measures, and Node Sizes on EEG Source Network: A Simultaneous EEG Study.

Brain network provides an essential perspective for studying normal and pathological brain activities. Reconstructing the brain network in the source space becomes more needed, for example, as a target in non-invasive neuromodulation. Precise estimating source activities from the scalp EEG is still challenging because it is an ill-posed question and because of the volume conduction effect. There is no consensus on how to reconstruct the EEG source network. This study uses simultaneous scalp EEG and stereo-EEG to investigate the effect of inverse solutions, connectivity measures, and node sizes on the reconstruction of the source network. We evaluated the performance of different methods on both source activity and network. Numerical simulation was also carried out for comparison. The weighted phase-lag index (wPLI) method achieved significantly better performance on the reconstructed networks in source space than five other connectivity measures (directed transfer function (DTF), partial directed coherence (PDC), efficient effective connectivity (EEC), Pearson correlation coefficient (PCC), and amplitude envelope correlation (AEC)). There is no significant difference between the inverse solutions (standardized low-resolution brain electromagnetic tomography (sLORETA), weighted minimum norm estimate (wMNE), and linearly constrained minimum variance (LCMV) beamforming) on the reconstructed source networks. The source network based on signal phases can fit intracranial activities better than signal waveform properties or causality. Our study provides a basis for reconstructing source space networks from scalp EEG, especially for future neuromodulation research.

Smooth Tensor Qatar Riyal Decomposition for Dynamic MRI Reconstruction.

Dynamic magnetic resonance imaging (dMRI) speed and imaging quality have always been a crucial issue in medical imaging research. Most existing methods characterize the tensor rank-based minimization to reconstruct dMRI from sampling k- t space data. However, (1) these approaches that unfold the tensor along each dimension destroy the inherent structure of dMR images. (2) they focus on preserving global information only, while ignoring the local details reconstruction such as the spatial piece-wise smoothness and sharp boundaries. To overcome these obstacles, we suggest a novel low-rank tensor decomposition approach by integrating tensor Qatar Riyal (QR) decomposition, low-rank tensor nuclear norm, and asymmetric total variation to reconstruct dMRI, named TQRTV. Specifically, while preserving the tensor inherent structure by utilizing tensor nuclear norm minimization to approximate tensor rank, QR decomposition reduces the dimensions in the low-rank constraint term, thereby improving the reconstruction performance. TQRTV further exploits the asymmetric total variation regularizer to capture local details. Numerical experiments demonstrate that the proposed reconstruction approach is superior to the existing ones.

Efficient ADMM Algorithm for Atomic Norm Minimization in SAR Tomography

Efficient ADMM Algorithm for Atomic Norm Minimization in SAR Tomography

Traffic matrix completion by weighted tensor nuclear norm minimization and time slicing

Traffic matrix completion by weighted tensor nuclear norm minimization and time slicing

Support Matrix Machine via Joint l2,1 and Nuclear Norm Minimization Under Matrix Completion Framework for Classification of Corrupted Data.

Traditional support vector machines (SVMs) are fragile in the presence of outliers; even a single corrupt data point can arbitrarily alter the quality of the approximation. If even a small fraction of columns is corrupted, then classification performance will inevitably deteriorate. This article considers the problem of high-dimensional data classification, where a number of the columns are arbitrarily corrupted. An efficient Support Matrix Machine that simultaneously performs matrix Recovery (SSMRe) is proposed, i.e. feature selection and classification through joint minimization of l2,1 (the nuclear norm of L ). The data are assumed to consist of a low-rank clean matrix plus a sparse noisy matrix. SSMRe works under incoherence and ambiguity conditions and is able to recover an intrinsic matrix of higher rank in the presence of data densely corrupted. The objective function is a spectral extension of the conventional elastic net; it combines the property of matrix recovery along with low rank and joint sparsity to deal with complex high-dimensional noisy data. Furthermore, SSMRe leverages structural information, as well as the intrinsic structure of data, avoiding the inevitable upper bound. Experimental results on different real-time applications, supported by the theoretical analysis and statistical testing, show significant gain for BCI, face recognition, and person identification datasets, especially in the presence of outliers, while preserving a reasonable number of support vectors.

Atomic Norm Minimization Based Fast Off-Grid Tomographic SAR Imaging With Nonuniform Sampling

Atomic Norm Minimization Based Fast Off-Grid Tomographic SAR Imaging With Nonuniform Sampling

The Perturbation Analysis of Nonconvex Low-Rank Matrix Robust Recovery.

In this article, we bring forward a completely perturbed nonconvex Schatten p -minimization to address a model of completely perturbed low-rank matrix recovery (LRMR). This article based on the restricted isometry property (RIP) and the Schatten- p null space property (NSP) generalizes the investigation to a complete perturbation model thinking over not only noise but also perturbation, and it gives the RIP condition and the Schatten- p NSP assumption that guarantee the recovery of low-rank matrix and the corresponding reconstruction error bounds. In particular, the analysis of the result reveals that in the case that p decreases 0 and for the complete perturbation and low-rank matrix, the condition is the optimal sufficient condition (Recht et al., 2010). In addition, we study the connection between RIP and Schatten- p NSP and discern that Schatten- p NSP can be inferred from the RIP. The numerical experiments are conducted to show better performance and provide outperformance of the nonconvex Schatten p -minimization method comparing with the convex nuclear norm minimization approach in the completely perturbed scenario.

L0 Gradient-Regularization and Scale Space Representation Model for Cartoon and Texture Decomposition.

In this paper, we consider decomposing an image into its cartoon and texture components. Traditional methods, which mainly rely on the gradient amplitude of images to distinguish between these components, often show limitations in decomposing small-scale, high-contrast texture patterns and large-scale, low-contrast structural components. Specifically, these methods tend to decompose the former to the cartoon image and the latter to the texture image, neglecting the scale features inherent in both components. To overcome these challenges, we introduce a new variational model which incorporates an L0-based total variation norm for the cartoon component and an L2 norm for the scale space representation of the texture component. We show that the texture component has a small L2 norm in the scale space representation. We apply a quadratic penalty function to handle the non-separable L0 norm minimization problem. Numerical experiments are given to illustrate the efficiency and effectiveness of our approach.

Channel Estimation for RIS-Aided MIMO Systems: A Partially Decoupled Atomic Norm Minimization Approach

Channel Estimation for RIS-Aided MIMO Systems: A Partially Decoupled Atomic Norm Minimization Approach

Location-Aware Beam Training and Multi-Dimensional ANM-Based Channel Estimation for RIS-Aided mmWave Systems

In this paper, we propose a location-aware channel estimation based on the atomic norm minimization (ANM) for the reconfigurable intelligent surface (RIS)-aided millimeter-wave multiple-input-multiple-output (MIMO) systems. The beam training overhead at the base station (BS) is reduced by the direct beam steering towards the RIS with the location of the BS and the RIS. The RIS beamwidth adaptation is proposed to reduce the beam training overhead at the RIS, and also it enables accurate channel estimation by ensuring the user equipment receives all the multipath components from the RIS. After the beam training, the cascaded effective channel of the RIS-aided MIMO systems is estimated by ANM. Depending on whether the beam training overhead at the BS or at the RIS is reduced or not, the channel is represented as a linear combination of either 1D atoms, 2D atoms, or 3D atoms, and the ANM is applied to estimate the channel. Simulation results show that the proposed location-aware channel estimation via 2D ANM and 3D ANM achieves superior estimation accuracy to benchmarks.

Time-Delay Estimation of Ground-Penetrating Radar Using Co-Prime Sampling Strategy via Atomic Norm Minimization

Time-Delay Estimation of Ground-Penetrating Radar Using Co-Prime Sampling Strategy via Atomic Norm Minimization

STP method for solving the minimal norm Toeplitz solutions of MX-~XN=GY+R

STP method for solving the minimal norm Toeplitz solutions of MX-~XN=GY+R

Minimal time sampled-data controls for the ordinary differential system

In this paper, we design a minimal time optimal control problem for an ordinary differential system with sampled-data controls, and use it to approximate a time optimal control problem for the ordinary differential system with distributed controls. We find connections among this problem, a minimal norm sampled-data control problem and a minimization problem, and obtain some properties on these problems. Based on these, we not only build up error estimates for optimal time and optimal controls between the minimal time sampled-data control problem and the minimal time distributed control problem, in terms of the sampling period, but we also prove that such estimates are optimal in some sense.

EFFICIENCY OF AMIDES AS CRYOPROTECTORS IN THE COMPOSITION OF PROTECTIVE ENVIRONMENTS FOR BULLS SPERM CRYOCONSERVATION

The article highlights the results of research on the effectiveness of the introduction of cryoprotectants of the amide group – dimethylformamide (DMF), dimethylacetamide (DMAC) into the cryoprotective media for bull sperm and to determine their effect on the main physiological characteristics of germ cells. Materials and methods. Immediately after obtaining sperm, it was diluted with medium No. 1 containing 5.6% glycerol and 1.4% DMF (experimental group 1). Experimental group 2 was also diluted and treated with medium No. 1, but with the addition of 5.6% glycerol and 1.4% DMAC. After saturation of the sperm with the protective substances of medium № 1, it was diluted with medium No 2 containing 4% glycerol and 1% DMF (experimental group 1) and 4% glycerol and 1% DMAC (experimental group 2). Control samples were diluted according to a standard two-moment protocol using 7% glycerol in medium No. 1 and 5% glycerol in medium No. 2. Cryopreservation of spermatozoid was carried out by direct immersion of standard flat metal cassettes with coated granules in a liquid nitrogen medium. At the same time, cooling was carried out in the following mode: 4°C to minus 10°C at minus 3°C/min and from minus 10°C to minus 80°C at minus 40°C/min. Deconservation of spermatozoa was carried out at a temperature of 38–39°C. Cows were inseminated by the recto-cervical method. The results. The use of penetrating cryoprotectants from the amide group - dimethylformamide and dimethylacetamide - in media for sperm dilution and cryopreservation ensures a certain increase in the motility of germcells by 5.9% and 9.0%, respectively. The positive effect of the composition of cryoprotectants was also noted regarding the survivat of sperm after deconservation. Thus, the survival rate in the second experimental group was 0.67 hours or 10.3% higher than in the control group. The environments supplemented with cryoprotective substances of the amide group ensured sufficiently high sperm survival at body temperature (38ºС), which significantly exceeded the established minimum physiological norm (5 hours). In percentage terms, this excess was 34.6% and 42.6%. Conclusions. The feasibility of using combinations of endocellular cryoprotectants made from glycerol and dimethylformamide (DMF) or glycerol and dimethylacetamide (DMAC) in cryoprotective media (diluents) for bull sperm has been proven, which increases the quality characteristics of the biomaterial.

Solution of the EEG inverse problem by random dipole sampling

Electroencephalography (EEG) source imaging aims to reconstruct brain activity maps from the neuroelectric potential difference measured on the skull. To obtain the brain activity map, we need to solve an ill-posed and ill-conditioned inverse problem that requires regularization techniques to make the solution viable. When dealing with real-time applications, dimensionality reduction techniques can be used to reduce the computational load required to evaluate the numerical solution of the EEG inverse problem. To this end, in this paper we use the random dipole sampling method, in which a Monte Carlo technique is used to reduce the number of neural sources. This is equivalent to reducing the number of the unknowns in the inverse problem and can be seen as a first regularization step. Then, we solve the reduced EEG inverse problem with two popular inversion methods, the weighted Minimum Norm Estimate (wMNE) and the standardized LOw Resolution brain Electromagnetic TomogrAphy (sLORETA). The main result of this paper is the error estimates of the reconstructed activity map obtained with the randomized version of wMNE and sLORETA. Numerical experiments on synthetic EEG data demonstrate the effectiveness of the random dipole sampling method.

ADMM-Net for Beamforming Based on Linear Rectification with the Atomic Norm Minimization

Target misalignment can cause beam pointing deviations and degradation of sidelobe performance. In order to eliminate the effect of target misalignment, we formulate the jamming sub-space recovery problem as a linearly modified atomic norm-based optimization. Then, we develop a deep-unfolding network based on the alternating direction method of multipliers (ADMM), which effectively improves the applicability and efficiency of the algorithm. By using the back-propagation process of deep-unfolding networks, the proposed method could optimize the hyper-parameters in the original atomic norm. This feature enables the adaptive beamformer to adjust its weight according to the observed data. Specifically, the proposed method could determine the optimal hyper-parameters under different interference noise matrix conditions. Simulation results demonstrate that the proposed network could reduce computational cost and achieve near-optimal performance with low complexity.

Optimal Joint Path Planning of a New Virtual-Linkage-Based Redundant Finishing Stage for Additive-Finishing Integrated Manufacturing

This paper describes the optimal path planning of a redundant finishing mechanism developed for joint space-based additive-finishing integrated manufacturing (AFM). The research motivation results from an inevitable one-sided layout of a finishing stage (FS) with regard to the additive stage (AS) in the AFM. These two stages share a 2-dof bed stage (BS), and the FS can lightly shave off the rough-surfaced 3D print on the bed. Since the FS located at the side of the AS cannot reach all the target points of the 3D print, the bed should be able to rotate the 3D print about the z-axis and translate it in the z-axis. As a result, the AS has 4-dof joints for 2P and 1P1R during the additive process with AS-BS, and FS has 4-dof and 2-dof integrated joints for 2P2R and 1P1R during the finishing process with FS-BS, respectively. For the kinematic modeling of the FS part and the BS, the virtual linkage connecting the bed frame origin and the FS’s joint frame for approaching the BS is considered to realize seamless kinematic redundancy. The minimum Euclidian norm of the joint velocity space is the objective function to find the optimal joint space solution for a given tool path. To confirm the feasibility of the developed joint path planning algorithm in the proposed FS-BS mechanism, layer-by-layer slicing of a given 3D print’s CAD model and tool path generation were performed. Then, the numerical simulations of the optimal joint path planning for some primitive 3D print geometries were conducted. As a result, we confirmed that the maximum and mean pose error in point-by-point only, with the developed optimal joint path planning algorithm, were less than 202 nm and 153 nm, respectively. Since precision and general machining accuracies in tool path generation are in the range of ±10 μm and 20 μm, the pose error in this study fully satisfies the industry requirements.

Industrial computed tomography for three-dimensional cultural relic model reconstruction based on L1-αL2+TV norm minimization

Industrial computed tomography (ICT) has emerged as a valuable tool for the conservation of cultural relics since it enables the extraction of information about the internal structure of artifacts without causing any damage. However, sparse and finite angle projection computed tomography (CT) often generates images with a large number of artifacts caused by insufficient data. This paper introduces a new cone-beam CT hybrid model based on compressed sensing (CS) theory and total variance (TV) denoising using the Split Bregman algorithm to address this problem, for the first time using compressed sensing theory for CT reconstruction of cultural relics. The model combines the L1 and L2 norms and optimizes the total variance of the image as the objective function. To enhance the reconstruction of L1-L2, the paper employs the continuation strategy of α and proposes a new combination function to update α. Consequently, the reconstruction results are compared with those of traditional common methods, and the effect of different α update functions is observed on the reconstruction results. The results from the model and real CT images demonstrate that the proposed L1-αL2 + TV method yields superior reconstruction results compared to ART + TV, SART, and L1/L2 algorithms based on objective evaluation indexes such as RMSE, SSIM, and PSNR, the proposed L1-αL2 + TV method achieves SSIM improvement of at least 15.2 %. Moreover, the newly proposed combined function is better at preserving the grain of the image, resulting in a much-improved reconstruction of the contours, making it highly beneficial for subsequent conservation and restoration of heritage. Overall, this proposed L1-αL2 + TV mixture model provides low-noise and high-quality reconstruction results, while maintaining the grain of the original image, making it a great boon for heritage conservation and restoration.

Reweighted robust and discriminative latent subspace projection for face recognition

Subspace projection has been widely studied to implement the feature extraction for face recognition. However, it scarcely facilitates exploring the label information in the subspace projection procedure. The feature extraction and classification are usually divided into two separate procedures. This fails to explore the discriminative information from the training data, and thus degrades the discrimination of the extracted features and lowers the face recognition accuracy. To address this issue, we present a novel reweighted robust and discriminative latent subspace projection (ReRDLSP) method which organically integrates the reweighted latent low-rank representation model and discriminative ridge regression into a union framework. We employ a reweighted nuclear norm minimization to realize the low-rank regularization, which provides adaptive weighted values assignment, regularizes the representation matrix adaptively, and thus boosts the capability and flexibility of the method. Moreover, a discriminative ridge regression method is presented by employing a nonnegative relaxation, which enlarges the margins of the face samples from different classes as much as possible and boosts the freedom of fitting the label information. The computational complexity and convergence analysis are also discussed in detail. Extensive experiments are demonstrated and very promising results are achieved compared with some state-of-the-art face recognition methods.