Approximate estimation of cell-type resolution transcriptome in bulk tissue through matrix completion.

Single-cell RNA sequencing (scRNA-seq) has emerged as a powerful tool for uncovering cellular heterogeneity. However, the high costs associated with this technique have rendered it impractical for studying large patient cohorts. We introduce ENIGMA (Deconvolution based on Regularized Matrix Completion), a method that addresses this limitation through accurately deconvoluting bulk tissue RNA-seq data into a readout with cell-type resolution by leveraging information from scRNA-seq data. By employing a matrix completion strategy, ENIGMA minimizes the distance between the mixture transcriptome obtained with bulk sequencing and a weighted combination of cell-type-specific expression. This allows the quantification of cell-type proportions and reconstruction of cell-type-specific transcriptomes. To validate its performance, ENIGMA was tested on both simulated and real datasets, including disease-related tissues, demonstrating its ability in uncovering novel biological insights.

DURIAN: an integrative deconvolution and imputation method for robust signaling analysis of single-cell transcriptomics data.

Single-cell RNA sequencing trades read-depth for dimensionality, often leading to loss of critical signaling gene information that is typically present in bulk data sets. We introduce DURIAN (Deconvolution and mUltitask-Regression-based ImputAtioN), an integrative method for recovery of gene expression in single-cell data. Through systematic benchmarking, we demonstrate the accuracy, robustness and empirical convergence of DURIAN using both synthetic and published data sets. We show that use of DURIAN improves single-cell clustering, low-dimensional embedding, and recovery of intercellular signaling networks. Our study resolves several inconsistent results of cell-cell communication analysis using single-cell or bulk data independently. The method has broad application in biomarker discovery and cell signaling analysis using single-cell transcriptomics data sets.

Transient Interference Excision and Spectrum Reconstruction with Partial Samples Using Modified Alternating Direction Method of Multipliers-Net for the Over-the-Horizon Radar.

Transient interference often submerges the actual targets when employing over-the-horizon radar (OTHR) to detect targets. In addition, modern OTHR needs to carry out multi-target detection from sea to air, resulting in the sparse sampling of echo data. The sparse OTHR signal will raise serious grating lobes using conventional methods and thus degrade target detection performance. This article proposes a modified Alternating Direction Method of Multipliers (ADMM)-Net to reconstruct the target and clutter spectrum of sparse OTHR signals so that target detection can be performed normally. Firstly, transient interferences are identified based on the sparse basis representation and then excised. Therefore, the processed signal can be seen as a sparse OTHR signal. By solving the Doppler sparsity-constrained optimization with the trained network, the complete Doppler spectrum is reconstructed effectively for target detection. Compared with traditional sparse solution methods, the presented approach can balance the efficiency and accuracy of OTHR signal spectrum reconstruction. Both simulation and real-measured OTHR data proved the proposed approach's performance.

Efficient Aperture Fill Time Correction for Wideband Sparse Array Using Improved Variable Fractional Delay Filters.

To solve the problem of aperture fill time (AFT) for wideband sparse arrays, variable fractional delay (VFD) FIR filters are applied to eliminate linear coupling between spatial and time domains. However, the large dimensions of the filter coefficient matrix result in high system complexity. To alleviate the computational burden of solving VFD filter coefficients, a novel multi-regultion minimax (MRMM) model utilizing the sparse representation technique has been presented. The error function is constrained by the introduction of L2-norm and L1-norm regularizations within the minimax criterion. The L2-norm effectively resolves the problems of overfitting and non-unique solutions that arise in the sparse optimization of traditional minimax (MM) models. Meanwhile, the use of multiple L1-norms enables the optimal design of the smallest sub-filter number and order of the VFD filter. To solve the established nonconvex model, an improved sequential-alternating direction method of multipliers (S-ADMM) algorithm for filter coefficients is proposed, which utilizes sequential alternation to iteratively update multiple soft-thresholding problems. The experimental results show that the optimized VFD filter reduces system complexity significantly and corrects AFT effectively in a wideband sparse array.

A Sparse Recovery Algorithm for Suppressing Multiple Linear Frequency Modulation Interference in the Synthetic Aperture Radar Image Domain.

In synthetic aperture radar (SAR) signal processing, compared with the raw data of level-0, level-1 SAR images are more readily accessible and available in larger quantities. However, an amount of level-1 images are affected by radio frequency interference (RFI), which typically originates from Linear Frequency Modulation (LFM) signals emitted by ground-based radars. Existing research on interference suppression in level-1 data has primarily focused on two methods: transforming SAR images into simulated echo data for interference suppression, or focusing interference in the frequency domain and applying notching filters to reduce interference energy. However, these methods overlook the effective utilization of the interference parameters or are confined to suppressing only one type of LFM interference at a time. In certain SAR images, multiple types of LFM interference manifest bright radiation artifacts that exhibit varying lengths along the range direction while remaining constant in the azimuth direction. It is necessary to suppress multiple LFM interference on SAR images when original echo data are unavailable. This article proposes a joint sparse recovery algorithm for interference suppression in the SAR image domain. In the SAR image domain, two-dimensional LFM interference typically exhibits differences in parameters such as frequency modulation rate and pulse width in the range direction, while maintaining consistency in the azimuth direction. Based on this observation, this article constructs a series of focusing operators for LFM interference in SAR images. These operators enable the sparse representation of dispersed LFM interference. Subsequently, an optimization model is developed that can effectively suppress multi-LFM interference and reduce image loss with the assistance of a regularization term in the image domain. Simulation experiments conducted in various scenarios validate the superior performance of the proposed method.

Fast Fusion Clustering via Double Random Projection.

In unsupervised learning, clustering is a common starting point for data processing. The convex or concave fusion clustering method is a novel approach that is more stable and accurate than traditional methods such as k-means and hierarchical clustering. However, the optimization algorithm used with this method can be slowed down significantly by the complexity of the fusion penalty, which increases the computational burden. This paper introduces a random projection ADMM algorithm based on the Bernoulli distribution and develops a double random projection ADMM method for high-dimensional fusion clustering. These new approaches significantly outperform the classical ADMM algorithm due to their ability to significantly increase computational speed by reducing complexity and improving clustering accuracy by using multiple random projections under a new evaluation criterion. We also demonstrate the convergence of our new algorithm and test its performance on both simulated and real data examples.

Computational drug repositioning based on multi-similarities bilinear matrix factorization.

With the development of high-throughput technology and the accumulation of biomedical data, the prior information of biological entity can be calculated from different aspects. Specifically, drug-drug similarities can be measured from target profiles, drug-drug interaction and side effects. Similarly, different methods and data sources to calculate disease ontology can result in multiple measures of pairwise disease similarities. Therefore, in computational drug repositioning, developing a dynamic method to optimize the fusion process of multiple similarities is a crucial and challenging task. In this study, we propose a multi-similarities bilinear matrix factorization (MSBMF) method to predict promising drug-associated indications for existing and novel drugs. Instead of fusing multiple similarities into a single similarity matrix, we concatenate these similarity matrices of drug and disease, respectively. Applying matrix factorization methods, we decompose the drug-disease association matrix into a drug-feature matrix and a disease-feature matrix. At the same time, using these feature matrices as basis, we extract effective latent features representing the drug and disease similarity matrices to infer missing drug-disease associations. Moreover, these two factored matrices are constrained by non-negative factorization to ensure that the completed drug-disease association matrix is biologically interpretable. In addition, we numerically solve the MSBMF model by an efficient alternating direction method of multipliers algorithm. The computational experiment results show that MSBMF obtains higher prediction accuracy than the state-of-the-art drug repositioning methods in cross-validation experiments. Case studies also demonstrate the effectiveness of our proposed method in practical applications. Availability: The data and code of MSBMF are freely available at https://github.com/BioinformaticsCSU/MSBMF. Corresponding author: Jianxin Wang, School of Computer Science and Engineering, Central South University, Changsha, Hunan 410083, P. R. China. E-mail: jxwang@mail.csu.edu.cn Supplementary Data: Supplementary data are available online at https://academic.oup.com/bib.

Block-Active ADMM to Minimize NMF with Bregman Divergences.

Over the last ten years, there has been a significant interest in employing nonnegative matrix factorization (NMF) to reduce dimensionality to enable a more efficient clustering analysis in machine learning. This technique has been applied in various image processing applications within the fields of computer vision and sensor-based systems. Many algorithms exist to solve the NMF problem. Among these algorithms, the alternating direction method of multipliers (ADMM) and its variants are one of the most popular methods used in practice. In this paper, we propose a block-active ADMM method to minimize the NMF problem with general Bregman divergences. The subproblems in the ADMM are solved iteratively by a block-coordinate-descent-type (BCD-type) method. In particular, each block is chosen directly based on the stationary condition. As a result, we are able to use much fewer auxiliary variables and the proposed algorithm converges faster than the previously proposed algorithms. From the theoretical point of view, the proposed algorithm is proved to converge to a stationary point sublinearly. We also conduct a series of numerical experiments to demonstrate the superiority of the proposed algorithm.

TDFusion: When Tensor Decomposition Meets Medical Image Fusion in the Nonsubsampled Shearlet Transform Domain.

In this paper, a unified optimization model for medical image fusion based on tensor decomposition and the non-subsampled shearlet transform (NSST) is proposed. The model is based on the NSST method and the tensor decomposition method to fuse the high-frequency (HF) and low-frequency (LF) parts of two source images to obtain a mixed-frequency fused image. In general, we integrate low-frequency and high-frequency information from the perspective of tensor decomposition (TD) fusion. Due to the structural differences between the high-frequency and low-frequency representations, potential information loss may occur in the fused images. To address this issue, we introduce a joint static and dynamic guidance (JSDG) technique to complement the HF/LF information. To improve the result of the fused images, we combine the alternating direction method of multipliers (ADMM) algorithm with the gradient descent method for parameter optimization. Finally, the fused images are reconstructed by applying the inverse NSST to the fused high-frequency and low-frequency bands. Extensive experiments confirm the superiority of our proposed TDFusion over other comparison methods.

Destriping of Remote Sensing Images by an Optimized Variational Model.

Satellite sensors often capture remote sensing images that contain various types of stripe noise. The presence of these stripes significantly reduces the quality of the remote images and severely affects their subsequent applications in other fields. Despite the existence of many stripe noise removal methods in the research, they often result in the loss of fine details during the destriping process, and some methods even generate artifacts. In this paper, we proposed a new unidirectional variational model to remove horizontal stripe noise. The proposed model fully considered the directional characteristics and structural sparsity of the stripe noise, as well as the prior features of the underlying image, to design different sparse constraints, and the ℓp quasinorm was introduced in these constraints to better describe these sparse characteristics, thus achieving a more excellent destriping effect. Moreover, we employed the fast alternating direction method of multipliers (ADMM) to solve the proposed non-convex model. This significantly improved the efficiency and robustness of the proposed method. The qualitative and quantitative results from simulated and real data experiments confirm that our method outperforms existing destriping approaches in terms of stripe noise removal and preservation of image details.

Fast Trajectory Tracking Control Algorithm for Autonomous Vehicles Based on the Alternating Direction Multiplier Method (ADMM) to the Receding Optimization of Model Predictive Control (MPC).

In order to improve the real-time performance of the trajectory tracking of autonomous vehicles, this paper applies the alternating direction multiplier method (ADMM) to the receding optimization of model predictive control (MPC), which improves the computational speed of the algorithm. Based on the vehicle dynamics model, the output equation of the autonomous vehicle trajectory tracking control system is constructed, and the auxiliary variable and the dual variable are introduced. The quadratic programming problem transformed from the MPC and the vehicle dynamics constraints are rewritten into the solution of the ADMM form, and a decreasing penalty factor is used during the solution process. The simulation verification is carried out through the joint simulation platform of Simulink and Carsim. The results show that, compared with the active set method (ASM) and the interior point method (IPM), the algorithm proposed in this paper can not only improve the accuracy of trajectory tracking, but also exhibits good real-time performance in different prediction time domains and control time domains. When the prediction time domain increases, the calculation time shows no significant difference. This verifies the effectiveness of the ADMM in improving the real-time performance of MPC.

An Innovative Approach for Removing Stripe Noise in Infrared Images.

The non-uniformity of infrared detectors' readout circuits can lead to stripe noise in infrared images, which affects their effective information and poses challenges for subsequent applications. Traditional denoising algorithms have limited effectiveness in maintaining effective information. This paper proposes a multi-level image decomposition method based on an improved LatLRR (MIDILatLRR). By utilizing the global low-rank structural characteristics of stripe noise, the noise and smooth information are decomposed into low-rank part images, and texture information is adaptively decomposed into several salient part images, thereby better preserving texture edge information in the image. Sparse terms are constructed according to the smoothness of the effective information in the final low-rank part of the image and the sparsity of the stripe noise direction. The modeling of stripe noise is achieved using multi-sparse constraint representation (MSCR), and the Alternating Direction Method of Multipliers (ADMM) is used for calculation. Extensive experiments demonstrated the proposed algorithm's effectiveness and compared it with state-of-the-art algorithms in subjective judgments and objective indicators. The experimental results fully demonstrate the proposed algorithm's superiority and efficacy.

Delay Minimization in RIS-Assisted URLLC Systems under Reliability Constraints.

The ultra-reliable and low-latency communication (URLLC) systems are expected to support the stringent quality of service (QoS) demands in the Internet of Things (IoT) networks. In order to support the strict latency and reliability constraints, it is preferable to deploy a reconfigurable intelligent surface (RIS) in the URLLC systems to improve the link quality. In this paper, we focus on the uplink of an RIS-assisted URLLC system, and we propose to minimize the transmission latency under the reliability constraints. To solve the non-convex problem, a low-complexity algorithm is proposed by using the Alternating Direction Method of Multipliers (ADMM) technique. The RIS phase shifts optimization, which is typically non-convex, is efficiently solved by formulating as a Quadratically Constrained Quadratic Programming (QCQP) problem. Simulation results verify that our proposed ADMM-based method is able to achieve better performance than the conventional semi-definite relaxation (SDR)-based method with lower computational complexity. Our proposed RIS-assisted URLLC system is able to significantly reduce the transmission latency, which highlights the great potential in deploying RIS in the IoT networks with strict reliability requirements.

Alternating Direction Method of Multipliers-Based Constant Modulus Waveform Design for Dual-Function Radar-Communication Systems.

In this paper, we design constant modulus waveforms for dual-function radar-communication (DFRC) systems based on a multi-input multi-output (MIMO) configuration of sensors for a far-field scenario. At first, we formulate a non-convex optimization problem subject to waveform synthesis for minimizing the interference power while maintaining a constant modulus constraint. Next, we solve this non-convex problem, iteratively, using the alternating direction method of multipliers (ADMM) algorithm. Importantly, the designed waveforms approximate a desired beampattern in terms of a high-gain radar beam and a slightly high gain communication beam while maintaining a desired low sidelobe level. The designed waveforms ensure an improved detection probability and an improved bit error rate (BER) for radar and communications parts, respectively. Finally, we demonstrate the effectiveness of the proposed method through simulation results.

Remote Sensing Image of The Landsat 8-9 Compressive Sensing via Non-Local Low-Rank Regularization with the Laplace Function.

Utilizing low-rank prior data in compressed sensing (CS) schemes for Landsat 8-9 remote sensing images (RSIs) has recently received widespread attention. Nevertheless, most CS algorithms focus on the sparsity of an RSI and ignore its low-rank (LR) nature. Therefore, this paper proposes a new CS reconstruction algorithm for Landsat 8-9 remote sensing images based on a non-local optimization framework (NLOF) that is combined with non-convex Laplace functions (NCLF) used for the low-rank approximation (LAA). Since the developed algorithm is based on an approximate low-rank model of the Laplace function, it can adaptively assign different weights to different singular values. Moreover, exploiting the structural sparsity (SS) and low-rank (LR) between the image patches enables the restored image to obtain better CS reconstruction results of Landsat 8-9 RSI than the existing models. For the proposed scheme, first, a CS reconstruction model is proposed using the non-local low-rank regularization (NLLRR) and variational framework. Then, the image patch grouping and Laplace function are used as regularization/penalty terms to constrain the CS reconstruction model. Finally, to effectively solve the rank minimization problem, the alternating direction multiplier method (ADMM) is used to solve the model. Extensive numerical experimental results demonstrate that the non-local variational framework (NLVF) combined with the low-rank approximate regularization (LRAR) method of non-convex Laplace function (NCLF) can obtain better reconstruction results than the more advanced image CS reconstruction algorithms. At the same time, the model preserves the details of Landsat 8-9 RSIs and the boundaries of the transition areas.

Weighted Sum Secrecy Rate Maximization for Joint ITS- and IRS-Empowered System.

In this work, we investigate a novel intelligent surface-assisted multiuser multiple-input single-output multiple-eavesdropper (MU-MISOME) secure communication network where an intelligent reflecting surface (IRS) is deployed to enhance the secrecy performance and an intelligent transmission surface (ITS)-based transmitter is utilized to perform energy-efficient beamforming. A weighted sum secrecy rate (WSSR) maximization problem is developed by jointly optimizing transmit power allocation, ITS beamforming, and IRS phase shift. To solve this problem, we transform the objective function into an approximated concave form by using the successive convex approximation (SCA) technique. Then, we propose an efficient alternating optimization (AO) algorithm to solve the reformulated problem in an iterative way, where Karush-Kuhn-Tucker (KKT) conditions, the alternating direction method of the multiplier (ADMM), and majorization-minimization (MM) methods are adopted to derive the closed-form solution for each subproblem. Finally, simulation results are given to verify the convergence and secrecy performance of the proposed schemes.

High-Performance Statistical Computing in the Computing Environments of the 2020s.

Technological advances in the past decade, hardware and software alike, have made access to high-performance computing (HPC) easier than ever. We review these advances from a statistical computing perspective. Cloud computing makes access to supercomputers affordable. Deep learning software libraries make programming statistical algorithms easy and enable users to write code once and run it anywhere-from a laptop to a workstation with multiple graphics processing units (GPUs) or a supercomputer in a cloud. Highlighting how these developments benefit statisticians, we review recent optimization algorithms that are useful for high-dimensional models and can harness the power of HPC. Code snippets are provided to demonstrate the ease of programming. We also provide an easy-to-use distributed matrix data structure suitable for HPC. Employing this data structure, we illustrate various statistical applications including large-scale positron emission tomography and ℓ1-regularized Cox regression. Our examples easily scale up to an 8-GPU workstation and a 720-CPU-core cluster in a cloud. As a case in point, we analyze the onset of type-2 diabetes from the UK Biobank with 200,000 subjects and about 500,000 single nucleotide polymorphisms using the HPC ℓ1-regularized Cox regression. Fitting this half-million-variate model takes less than 45 minutes and reconfirms known associations. To our knowledge, this is the first demonstration of the feasibility of penalized regression of survival outcomes at this scale.

A Novel Stripe Noise Removal Model for Infrared Images.

Infrared images often carry obvious streak noises due to the non-uniformity of the infrared detector and the readout circuit. These streak noises greatly affect the image quality, adding difficulty to subsequent image processing. Compared with current elimination algorithms for infrared stripe noises, our approach fully utilizes the difference between the stripe noise components and the actual information components, takes the gradient sparsity along the stripe direction and the global sparsity of the stripe noises as regular terms, and treats the sparsity of the components across the stripe direction as a fidelity term. On this basis, an adaptive edge-preserving operator (AEPO) based on edge contrast was proposed to protect the image edge and, thus, prevent the loss of edge details. The final solution was obtained by the alternating direction method of multipliers (ADMM). To verify the effectiveness of our approach, many real experiments were carried out to compare it with state-of-the-art methods in two aspects: subjective judgment and objective indices. Experimental results demonstrate the superiority of our approach.

Coding for Large-Scale Distributed Machine Learning.

This article aims to give a comprehensive and rigorous review of the principles and recent development of coding for large-scale distributed machine learning (DML). With increasing data volumes and the pervasive deployment of sensors and computing machines, machine learning has become more distributed. Moreover, the involved computing nodes and data volumes for learning tasks have also increased significantly. For large-scale distributed learning systems, significant challenges have appeared in terms of delay, errors, efficiency, etc. To address the problems, various error-control or performance-boosting schemes have been proposed recently for different aspects, such as the duplication of computing nodes. More recently, error-control coding has been investigated for DML to improve reliability and efficiency. The benefits of coding for DML include high-efficiency, low complexity, etc. Despite the benefits and recent progress, however, there is still a lack of comprehensive survey on this topic, especially for large-scale learning. This paper seeks to introduce the theories and algorithms of coding for DML. For primal-based DML schemes, we first discuss the gradient coding with the optimal code distance. Then, we introduce random coding for gradient-based DML. For primal-dual-based DML, i.e., ADMM (alternating direction method of multipliers), we propose a separate coding method for two steps of distributed optimization. Then coding schemes for different steps are discussed. Finally, a few potential directions for future works are also given.

Penalized and constrained LAD estimation in fixed and high dimension.

Recently, many literatures have proved that prior information and structure in many application fields can be formulated as constraints on regression coefficients. Following these work, we propose a L 1 penalized LAD estimation with some linear constraints in this paper. Different from constrained lasso, our estimation performs well when heavy-tailed errors or outliers are found in the response. In theory, we show that the proposed estimation enjoys the Oracle property with adjusted normal variance when the dimension of the estimated coefficients p is fixed. And when p is much greater than the sample size n, the error bound of proposed estimation is sharper than k log ( p ) / n . It is worth noting the result is true for a wide range of noise distribution, even for the Cauchy distribution. In algorithm, we not only consider an typical linear programming to solve proposed estimation in fixed dimension , but also present an nested alternating direction method of multipliers (ADMM) in high dimension. Simulation and application to real data also confirm that proposed estimation is an effective alternative when constrained lasso is unreliable.