Non-negative Least Squares Research Articles

Low-frequency noise characterization of gate oxide trap depth distribution of MOSFETs

To accurately obtain the depth distribution of the gate oxide traps that cause low-frequency noises, this study developed a discrete form of the low-frequency noise model in MOSFETs based on McWhorter's theory. The non-negative least squares (NNLS) method is employed to numerically solve the designed model. The low-frequency noises of planar Ge nMOSFETs with a gate stack match the prerequisite of the proposed form, which is dominated by carrier number fluctuations and is consistent with the McWhorter model. These transistors are used as the object of analysis in this study. By introducing a La2O3 cap layer to the gate stack, the gate oxide trap profiles calculated by the discrete model and the NNLS method showed obvious suppression of the traps in the HfO2 body and concentration of the traps in and near the SiO2/HfO2 interface. The research on both energy-dispersive x-ray spectroscopy and electron energy-loss spectroscopy has shown during annealing the diffusion of La into HfO2 and the appearance of La-rich layer at the SiO2/HfO2 interface in the Ge nMOSFET with a La2O3 cap. According to the existing first-principles calculations, the substitution of Hf in HfO2 by La increases the formation energy of oxygen vacancies, and the formation energy of oxygen vacancies in the HfnLamSixOy layer formed near the SiO2/HfO2 interface is lower than that of HfO2. The experimental and theoretical results support the physical connotation of the calculations and validate the solution proposed by this study.

Systems of Linear Equations with Non-Negativity Constraints: Hyper-Rectangle Cover Theory and Its Applications

In this paper, a novel hyper-rectangle cover theory is developed. Two important concepts, the cover order and the cover length, are introduced. We construct a specific échelon form of the matrix in the same manner as that employed to determine the rank of the matrix to obtain the cover order of any given matrix. Using the properties of the cover order, we obtain the necessary and sufficient conditions for the existence and uniqueness of the solutions for linear equations system with non-negativity constraints on variables for both homogeneous and nonhomogeneous cases. In addition, we apply the cover theory to analyze some typical problems in linear algebra and optimization with non-negativity constraints on variables, including linear programming (LP) problems and non-negative least squares (NNLS) problems. For LP problems, the three possible behaviours of the solutions are studied through cover theory. On the other hand, we develop a method to obtain the cover length of the covered variable. In this process, we discover the relationship between the cover length determination problem and the NNLS problem. This enables us to obtain an analytical optimal value for the NNLS problem.

Multispectral Imaging Method for Rapid Identification and Analysis of Paraffin-Embedded Pathological Tissues

The study of the interaction between light and biological tissue is of great help in the identification of diseases as well as structural alterations in tissues. In the present study, we have developed a tissue diagnostic technique by using multispectral imaging in the visible spectrum combined with principal component analysis (PCA). We used information from the propagation of light through paraffin-embedded tissues to assess differences in the eye tissues of control mouse embryos compared to mouse embryos whose mothers were deprived of folic acid (FA), a crucial vitamin necessary for the growth and development of the fetus. After acquiring the endmembers from the multispectral images, spectral unmixing was used to identify the abundances of those endmembers in each pixel. For each acquired image, the final analysis was performed by performing a pixel-by-pixel and wavelength-by-wavelength absorbance calculation. Non-negative least squares (NNLS) were used in this research. The abundance maps obtained for the first endmember revealed vascular alterations (vitreous and choroid) in the embryos with maternal FA deficiency. However, the abundance maps obtained for the third endmember showed alterations in the texture of some tissues such as the lens and retina. Results indicated that multispectral imaging applied to paraffin-embedded tissues enhanced tissue visualization. Using this method, first, it can be seen tissue damage location and then decide what kind of biological techniques to apply.

Structured channel covariance estimation from limited samples for large antenna arrays

In massive multiuser multiple antenna systems, the knowledge of the users’ channel covariance matrix is crucial for minimum mean square error channel estimation in the uplink and it plays an important role in several multiuser beamforming schemes in the downlink. Due to the large number of base station antennas, accurate covariance estimation is challenging especially in the case where the number of samples is limited and thus comparable to the channel vector dimension. As a result, the standard sample covariance estimator may yield a too large estimation error which in turn may yield significant system performance degradation with respect to the ideal channel covariance knowledge case. To address such problem, we propose a method based on a parametric representation of the channel angular scattering function. The proposed parametric representation includes a discrete specular component which is addressed using the well-known MUltiple SIgnal Classification (MUSIC) method, and a diffuse scattering component, which is modeled as the superposition of suitable dictionary functions. To obtain the representation parameters, we propose two methods, where the first solves a nonnegative least-squares problem and the second maximizes the likelihood function using expectation–maximization. Our simulation results show that the proposed methods outperform the state of the art with respect to various estimation quality metrics and different sample sizes.

A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data.

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. The results demonstrate the advantage of the algorithm in finding high-precision solutions.

Fast Sparse Non-Negative Least Squares via ADMM for High Resolution DOA Estimation

High-resolution and low-complexity direction of arrival (DOA) estimation deserves a warm welcome in a real radar sensor. However, achieving this goal is nontrivial. For the DOA estimation of the uniform linear array (ULA), we offer an efficient approach to reach a good compromise between complexity, resolution and accuracy. Under the covariance fitting framework, we construct a sparse non-negative least squares (NNLS) that is solved by the alternating direction method of multipliers (ADMM) at a low-computational complexity. The regularization item involved in the ADMM procedure yields an inherent improvement on robustness. Moreover, a large-scale matrix inversion that is a computationally expensive operation in the ADMM procedure is recursively computed by exploiting the diagonal matrix property of the regularization item, resulting in a reduction on complexity. In addition, the pre-estimation of the noise variance further reduces the scale of the sparse NNLS problem and alleviates the ill-conditioning effect to some extent. Compared to several sparse covariance fitting methods, both the simulation data and the 77 GHz radar-measured data demonstrate that the proposed algorithm has the good resolution, robustness, and accuracy performance with lower computationally cost.

The Lawson‐Hanson algorithm with deviation maximization: Finite convergence and sparse recovery

SummaryThe Lawson‐Hanson with Deviation Maximization (LHDM) method is a block algorithm for the solution of NonNegative Least Squares (NNLS) problems. In this work we devise an improved version of LHDM and we show that it terminates in a finite number of steps, unlike the previous version, originally developed for a special class of matrices. Moreover, we are concerned with finding sparse solutions of underdetermined linear systems by means of NNLS. An extensive campaign of experiments is performed in order to evaluate the performance gain with respect to the standard Lawson‐Hanson algorithm. We also show the ability of LHDM to retrieve sparse solutions, comparing it against several ‐minimization solvers in terms of solution quality and time‐to‐solution on a large set of dense instances.

Exemplar-Based Sparse Representations for Detection of Parkinson's Disease From Speech

Parkinson's disease (PD) is a progressive neurological disorder which affects the motor system. The automatic detection of PD improves the diagnosis of the disease, and it can be done in a non-invasive manner from speech. In this paper, we investigate the use of an exemplar-based sparse representation (SR) classification approach for detecting PD from speech. Exemplars are speech feature vectors extracted from the training data. The idea is to formulate the detection task as a problem of finding sparse representations of test speech feature vectors with respect to training speech exemplars. The main advantage of using the SR approach instead of conventional machine learning (ML)-based approaches is that the training step–which is time-consuming and sometimes requires unorganized hyper-parameter tuning–is not needed. Furthermore, SRs are more robust to redundancy and noise in the data. In this work, we study SR classification approaches based on two sparse coding models, namely, l1-regularized least squares ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> LS) and non-negative least squares (NNLS). We propose a strategy based on class-specific dictionaries for improving performance of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> LS- and NNLS-based SR classification. To investigate the detection performance, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> LS- and NNLS-based approaches are applied and compared with the traditional PD detection approach based on ML classification algorithms using the PC-GITA PD dataset and an openly available dataset consisting of mobile device voice recordings from healthy and PD patients. The results indicate that the proposed NNLS-based SR classification approach performs better than the traditional ML-based methods in discriminating PD patients from healthy subjects.

Weighted MMSE Precoding for Constructive Interference Region

In this letter, we propose a symbol-level precoding (SLP) design that aims to minimize the weighted mean square error between the received signal and the constellation point located in the constructive interference region (CIR). Unlike most existing SLP schemes that rely on channel state information (CSI) only, the proposed scheme exploits both CSI and the distribution information of the noise to achieve improved performance. We firstly propose a simple generic description of CIR that facilitates the subsequent SLP design. Such an objective can further be formulated as a nonnegative least squares (NNLS) problem, which can be solved efficiently by the active-set algorithm. Furthermore, the weighted minimum mean square error (WMMSE) precoding and the existing SLP can be easily verified as special cases of the proposed scheme. Finally, simulation results show that the proposed precoding outperforms the state-of-the-art SLP schemes in full signal-to-noise ratio ranges in both uncoded and coded systems without additional complexity over conventional SLP.

Miniaturizing a Chip-Scale Spectrometer Using Local Strain Engineering and Total-Variation Regularized Reconstruction.

A wafer-thin chip-scale portable spectrometer suitable for wearable applications based on a reconstructive algorithm was demonstrated. A total of 16 spectral encoders that simultaneously functioned as photodetectors were monolithically integrated on a chip area of 0.16 mm2 by applying local strain engineering in compressively strained InGaN/GaN multiple quantum well heterostructures. The built-in GaN pn junction enabled a direct photocurrent measurement. A non-negative least-squares (NNLS) algorithm with total-variation regularization and a choice of a proper kernel function was shown to deliver a decent spectral reconstruction performance in the wavelength range of 400-645 nm. The accuracies of spectral peak positions and intensity ratios between peaks were found to be 0.97% and 10.4%, respectively. No external optics, such as collimation optics and apertures, were used, enabled by angle-insensitive light-harvesting structures, including an array of cone-shaped backreflectors fabricated on the underside of the sapphire substrate.

Improvement in magnetic nanoparticle tomography estimation accuracy by combining sLORETA and non-negative least squares methods

Imaging methods that can detect biofunctionalized magnetic nanoparticles (MNPs) accumulated at cancerous tumor sites are expected to be part of the in vivo cancer diagnostic techniques. An imaging technique called magnetic nanoparticle tomography (MNT), which uses a magnetic sensor array, has been proposed. High sensitivity and spatial resolution were achieved using the non-negative least-squares (NNLS) inverse solution in MNT. However, owing to the presence of measurement noise, the concentration and position of certain MNPs were estimated inaccurately, i.e., artifacts were generated. To overcome this issue, this study first applied standardized low-resolution brain electromagnetic tomography (sLORETA), a spatial filter method with no location bias, to approximate the position of MNPs. The region of analysis was restricted to where the estimated value exceeded the threshold. Subsequently, the NNLS method was applied to estimate the concentration and position of MNPs in the restricted region. In the experiment, two Resovist MNP samples (300 or 500 μgFe) were arranged at a distance of 25–502 mm, and the concentration and position estimation were performed. The estimation results demonstrated that the proposed method successfully suppresses artifacts and adequately estimates the concentration and position of MNPs within a position error of 10 mm and a concentration error of 20 %.

Evaluation of a Gaussian dispersion transformation technique for tomographic mapping of the concentration field of atmospheric chemicals using multi-path optical remote sensing.

Horizontal radial plume mapping is a cost-effective optical remote sensing method for sensitive mapping concentration distribution of atmospheric chemicals in real time. However, its sparse sampling poses challenges for reconstruction algorithms. Neither non-smooth nor smooth algorithms can recover the realistic plume shape. A new approach called Gaussian dispersion transformation (GDT) has been proposed. It first reconstructs the emission rates from unknown sources. Then concentrations are calculated through a transformation matrix defined by a Gaussian dispersion model. Smoothness regularization is also applied during the reconstruction. The method was evaluated by using randomly generated maps. It shows significant improvement over a reconstructed plume shape. The nearness shows 72%-117% better than the non-negative least-square (NNLS) algorithm and 15%-26% better than the low third derivative (LTD) algorithm. A controlled-release field experiment of methane was also conducted. The realistic concentration distribution was calculated by using a Lagrangian stochastic dispersion model. The GDT algorithm successfully recovered the realistic plume shape. The nearness shows approximately 16% better than the NNLS and the LTD algorithms. Finally, a sensitivity analysis shows that the wind direction and atmospheric stability are the main parameters that affect the performance of the GDT algorithm.

GPU-accelerated connectome discovery at scale

Diffusion magnetic resonance imaging and tractography enable the estimation of anatomical connectivity in the human brain, in vivo. Yet, without ground-truth validation, different tractography algorithms can yield widely varying connectivity estimates. Although streamline pruning techniques mitigate this challenge, slow compute times preclude their use in big-data applications. We present ‘Regularized, Accelerated, Linear Fascicle Evaluation’ (ReAl-LiFE), a GPU-based implementation of a state-of-the-art streamline pruning algorithm (LiFE), which achieves >100× speedups over previous CPU-based implementations. Leveraging these speedups, we overcome key limitations with LiFE’s algorithm to generate sparser and more accurate connectomes. We showcase ReAl-LiFE’s ability to estimate connections with superlative test–retest reliability, while outperforming competing approaches. Moreover, we predicted inter-individual variations in multiple cognitive scores with ReAl-LiFE connectome features. We propose ReAl-LiFE as a timely tool, surpassing the state of the art, for accurate discovery of individualized brain connectomes at scale. Finally, our GPU-accelerated implementation of a popular non-negative least-squares optimization algorithm is widely applicable to many real-world problems.

Generating surface-offset common-image gathers with backward wavefield synthesis

Surface-offset common-image gathers (CIGs) are an important data format for seismic velocity analysis. However, the reverse time migration (RTM) method, which is wavefield propagation based, does not directly produce surface-offset CIGs because it propagates waves from all the offsets together. Here, we implement the generation of surface-offset CIGs by synthesizing the backward wavefields using the forward wavefields at locations where source and receiver locations overlap. This method produces surface-offset CIGs with high accuracy and low cost when compared with those generated by backpropagating each trace separately. We adopt nonnegative least-squares filters for sparse linear deconvolution. The computational effectiveness of the proposed method increases for higher dimensions, higher-order stencils, and more complicated wave equations. The proposed method works stably on a realistic towed-streamer acquisition system with moderate geometric positioning errors between the locations of airguns and hydrophones.

Deep Ensemble Machine Learning Framework for the Estimation of Concentrations.

Background:Accurate estimation of historical (particle matter with an aerodynamic diameter of less than ) is critical and essential for environmental health risk assessment.Objectives:The aim of this study was to develop a multiple-level stacked ensemble machine learning framework for improving the estimation of the daily ground-level concentrations.Methods:An innovative deep ensemble machine learning framework (DEML) was developed to estimate the daily concentrations. The framework has a three-stage structure: At the first stage, four base models [gradient boosting machine (GBM), support vector machine (SVM), random forest (RF), and eXtreme gradient boosting (XGBoost)] were used to generate a new data set of concentrations for training the next-stage learners. At the second stage, three meta-models [RF, XGBoost, and Generalized Linear Model (GLM)] were used to estimate concentrations using a combination of the original data set and the predictions from the first-stage models. At the third stage, a nonnegative least squares (NNLS) algorithm was employed to obtain the optimal weights for estimation. We took the data from 133 monitoring stations in Italy as an example to implement the DEML to predict daily at each grid cell from 2015 to 2019 across Italy. We evaluated the model performance by performing 10-fold cross-validation (CV) and compared it with five benchmark algorithms [GBM, SVM, RF, XGBoost, and Super Learner (SL)].Results:The results revealed that the prediction performance of DEML [coefficients of determination and root mean square error ] was superior to any benchmark models (with of 0.51, 0.76, 0.83, 0.70, and 0.83 for GBM, SVM, RF, XGBoost, and SL approach, respectively). DEML displayed reliable performance in capturing the spatiotemporal variations of in Italy.Discussion: The proposed DEML framework achieved an outstanding performance in estimation, which could be used as a tool for more accurate environmental exposure assessment. https://doi.org/10.1289/EHP9752

Ultrathin Optics-Free Spectrometer with Monolithically Integrated LED Excitation.

A semiconductor spectrometer chip with a monolithically integrated light-emitting diode was demonstrated. The spectrometer design was based on a computational reconstruction algorithm and a series of absorptive spectral filters directly built in to the photodetectors’ active regions. The result is the elimination of the need to employ external optics to control the incident angle of light. In the demonstration, an array of gallium nitride (GaN) based photodetectors with wavelength selectivity generated via the principle of local strain engineering were designed and fabricated. Additionally, a GaN based LED was monolithically integrated. An optical blocking structure was used to suppress the LED-photodetector interference and was shown to be essential for the spectroscopic functionality. A proof of concept using a reflection spectroscopy configuration was experimentally conducted to validate the feasibly of simultaneously operating the LED excitation light source and the photodetectors. Spectral reconstruction using a non-negative least squares (NNLS) algorithm enhanced with orthogonal matching pursuit was shown to reconstruct the signal from the reflection spectroscopy. Optics-free operation was also demonstrated.

In vivo Raman spectroscopy monitors cervical change during labor

Biochemical cervical change during labor is not well understood, in part, because of a dearth of technologies capable of safely probing the pregnant cervix invivo. The need for such a technology is 2-fold: (1) to gain a mechanistic understanding of the cervical ripening and dilation process and (2) to provide an objective method for evaluating the cervical state to guide clinical decision-making. Raman spectroscopy demonstrates the potential to meet this need, as it is a noninvasive optical technique that can sensitively detect alterations in tissue components, such as extracellular matrix proteins, lipids, nucleic acids, and blood, which have been previously established to change during the cervical remodeling process. We sought to demonstrate that Raman spectroscopy can longitudinally monitor biochemical changes in the laboring cervix to identify spectral markers of impending parturition. Overall, 30 pregnant participants undergoing either spontaneous or induced labor were recruited. The Raman spectra were acquired invivo at 4-hour intervals throughout labor until rupture of membranes using a Raman system with a fiber-optic probe. Linear mixed-effects models were used to determine significant (P<.05) changes in peak intensities or peak ratios as a function of time to delivery in the study population. A nonnegative least-squares biochemical model was used to extract the changing contributions of specific molecule classes over time. We detected multiple biochemical changes during labor, including (1) significant decreases in Raman spectral features associated with collagen and other extracellular matrix proteins (P=.0054) attributed to collagen dispersion, (2) an increase in spectral features associated with blood (P=.0372), and (3) an increase in features indicative of lipid-based molecules (P=.0273). The nonnegative least-squares model revealed a decrease in collagen contribution with time to delivery, an increase in blood contribution, and a change in lipid contribution. Our findings have demonstrated that invivo Raman spectroscopy is sensitive to multiple biochemical remodeling changes in the cervix during labor. Furthermore, invivo Raman spectroscopy may be a valuable noninvasive tool for objectively evaluating the cervix to potentially guide clinical management of labor.

MULTIPLE ENDMEMBER SPECTRAL MIXTURE ANALYSIS OF DESIS IMAGE TO IDENTIFY ROOFTOPS IN KIGALI

Abstract. The development and increase of multi and hyperspectral sensors in the recent years have significantly improved urban structure analysis and interpretation. The current study is the first to investigate the potential of DESIS hyperspectral images for the detection or identification of urban roof materials. After field campaigns in 2014, 2015 and 2018 to collect ground truth points and rooftops radiometric properties; a linear spectral mixture, implemented using a non-negative least squares (NNLS) regression based on the sequential coordinate-wise algorithm (SCA) was applied on a DESIS image from 2020 of Kigali city to identify the different rooftops material and color. Although results show that most endmembers were predicted with a very low probability, the study proved that the combination of spectral mixture and hyperspectral data such as DESIS have great potential in the detection of rootops material. The presented study also highlghted a number of challenges resulting from the choice of spectral mixture algorithm and colinearity between materials.

Europa’s Surface Water-ice Crystallinity and Correlations between Lineae and Hydrate Composition

Abstract Europa’s surface composition and evidence for cryovolcanic activity can provide insight into the properties and composition of the subsurface ocean, allowing the evaluation of its potential habitability. One promising avenue for revealing the surface processing and subsurface activity are the relative fractions of crystalline and amorphous water-ice observed on the surface, which are influenced by temperature, charged particle bombardment, vapor deposition, and cryovolcanic activity. The crystallinity observed on Europa’s leading hemisphere cannot be reproduced by thermophysical and particle flux modeling alone, indicating that there may be additional processes influencing the surface. We performed a spectral mixture analysis on hyperspectral image cubes from the Galileo Near-Infrared Mapping Spectrometer (NIMS) to identify how surface crystallinity is influenced by physical processing at a high spatial resolution scale. We focus specifically on two image cubes, 15e015 closer to the equator and 17e009 closer to the south pole, both on the leading hemisphere. We performed a nonnegative least-squares spectral mixture analysis to reveal both the non-ice composition and the water-ice crystallinity of the surface. We found that amorphous water-ice dominates the spectrum at the equator and the south pole. We estimated a mean crystallinity of ∼35% within the 15e015 NIMS cube and a mean crystallinity of ∼15% within the 17e009 NIMS cube, which is consistent with ground-based spectroscopically derived crystallinities. We also identified a correlation of magnesium sulfate, magnesium chloride, and hydrated sulfuric acid with lineae and ridges, which may provide evidence for surface processing by upwelling subsurface material.

BCUN: Bayesian Fully Convolutional Neural Network for Hyperspectral Spectral Unmixing

Spectral unmixing (SU) plays a fundamental role in hyperspectral image (HSI) processing. Effective SU relies on the accurate and efficient characterization of the noise effect, the endmembers, and the spatial correlation effect in abundances, as well as efficient optimization techniques to estimate these effects. To address these issues, this article presents a Bayesian fully convolutional hyperspectral unmixing network (BCUN) with the following key characteristics. First, a fully convolutional neural network (FCNN)-based deep image prior (DIP) is designed for enhanced characterization and estimation of the spatial context information in abundance maps, leading to more efficient and accurate abundance modeling than the traditional nonnegative least squares (NNLS) approaches. Second, a multivariate Gaussian distribution with an anisotropic covariance matrix is designed to characterize the conditional distribution of the spectral observations, leading to a novel Mahalanobis distance-based loss for FCNN training that is better capable of addressing the noise heterogeneous effect in HSI than the Euclidean distance-based mean squared error (MSE) loss in traditional deep neural networks. Third, the designed conditional distribution of spectral observations also enables the incorporation of the spectral mixture model (SMM) into the FCNN training process for effectively leveraging the knowledge in the forward spectral model. Fourth, the endmembers are modeled and estimated by a “purified means” approach that is capable of better characterizing endmembers. Finally, the above key components are coherently integrated into a Bayesian framework, and the resulting maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) problem is solved by a designed expectation–maximization (EM) algorithm. Experimental results on both simulated and real HSIs demonstrate that the proposed BCUN approach outperforms the other classical and state-of-the-art methods on both endmember estimation and abundance estimation.