Pose graph optimization (PGO) is fundamental to robot perception and navigation systems, serving as the mathematical backbone for solving simultaneous localization and mapping (SLAM). Existing solvers suffer from polynomial growth in computational complexity with graph size, hindering real-time deployment in large-scale scenarios. In this paper, by duplicating variables and introducing equality constraints, we reformulate the problem and propose a Parallelizable Riemannian Alternating Direction Method of Multipliers (PRADMM) to solve it efficiently. Compared with the state-of-the-art methods that usually exhibit polynomial time complexity growth with graph size, PRADMM enables efficient parallel computation across vertices regardless of graph size. Crucially, all subproblems admit closed-form solutions, ensuring PRADMM maintains exceptionally stable performance. Furthermore, by carefully exploiting the structures of the coefficient matrices in the constraints, we establish the global convergence of PRADMM under mild conditions, enabling larger relaxation step sizes within the interval (0,2). Extensive empirical validation on two synthetic datasets and multiple real-world 3D SLAM benchmarks confirms the superior computational performance of PRADMM.

Abstract. Hyperspectral and multispectral images fusion aims at integrating a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI) to construct a high-resolution hyperspectral image (HR-HSI). It is generally assumed that spatial blurring operator and spectral response operator are prior-known. However, such an assumption is extremely restrictive in practice. To overcome this limitation, this paper formulates blind fusion as a coupled inverse problem, integrating blind deconvolution in the spatial domain with blind unmixing in the spectral domain. From this novel perspective, we propose a unified tensor fusion framework capable of flexible self-adjustment and real-time fusion without pretraining. We further introduce an optimization model for the joint estimation of the target HR-HSI, the spatial point spread function, and the spectral response function. To solve this model, we devise a partially linearized alternating direction method of multipliers algorithm with Moreau envelope smoothing, accompanied by the rigorous convergence analysis. An initialization estimator tailored to the specific characteristics of the fusion problem is proposed. Numerical comparisons with state-of-the-art methods on both synthetic and real-world datasets demonstrate the compelling performance of the proposed method.

Abstract. This paper focuses on the convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems whose objective function is the sum of one weakly convex and two strongly convex functions. Many applications in image denoising and machine learning fields with a sparsity-driven regularization term can be approximated unbiasedly by weakly convex functions. Our new theoretical results provide convergence guarantees of the direct extension of ADMM (E-ADMM) without Lipschitz continuity of the gradient and Kurdyka–Łojasiewicz property, and establish the worst-case [Formula: see text] convergence rate in the nonergodic sense. Under further conditions such as Lipschitz continuity and nonsingularity, we derive the global linear rate of convergence. The numerical results on tensor robust principal component analysis and generalized elastic net regression illustrate that E-ADMM is efficient compared with some popular methods such as the difference-of-convex approach and accelerated proximal gradient descent.

This paper presents a new multiple-input multiple-output (MIMO) communication system. The system, termed as “pseudo MIMO”, facilitates the transmission of more parallel data streams than the number of receiving radio frequency (RF) chains. The key principle involves connecting multiple antenna elements to each receiving RF chain and employing multiple analog combining patterns for signal reception within the orthogonal frequency division multiplexing (OFDM) sampling period. Through detailing the entire transmission and signal processing procedures by matrix manipulation, the equivalent channel matrix for each OFDM subcarrier is derived in a unified matrix form, which can be further represented by the product of the analog combining matrix and the frequency domain wireless channel matrix. As per the equivalent channel matrix, an optimization problem is formulated and solved to maximize the spectral efficiency by jointly designing the digital precoding and analog combining matrices. Numerical results demonstrate that the performance of a pseudo MIMO system can closely approach that of a fully digital (FD) MIMO system with the same antenna configuration but more RF chains. It is also revealed that a low-precision discrete analog combining scheme is sufficient to achieve nearly optimal performance. Further, the effectiveness of pseudo MIMO technology is validated through prototype testing.

In this paper, we explore a specific optimization problem that involves the combination of a differentiable nonconvex function and a nondifferentiable function. The differentiable component lacks a global Lipschitz continuous gradient, posing challenges for optimization. To address this issue and accelerate the convergence, we propose a Bregman proximal stochastic gradient method with extrapolation (BPSGE), which only requires smooth adaptivity of the differentiable part. Under variance reduction framework, we not only analyze the subsequential and global convergence of the proposed algorithm under certain conditions, but also analyze the sublinear convergence rate of the subsequence, and the complexity of the algorithm, revealing that the BPSGE algorithm requires at most O(epsilon\^\,(-2)) iterations in expectation to attain an epsilon-stationary point. To validate the effectiveness of our proposed algorithm, we conduct numerical experiments on three real-world applications: graph regularized nonnegative matrix factorization (NMF), matrix factorization with weakly-convex regularization, and NMF with nonconvex sparsity constraints. These experiments demonstrate that BPSGE is faster than the baselines without extrapolation. The code is available at: https://github.com/nothing2wang/BPSGE-Algorithm.

Systematic and scientific training is an essential aspect of improving athletes' performance and has garnered significant attention. Athletes are continuously seeking new technologies to aid in training and prevent injuries. Digital twin technology, which integrates the Internet of things (IoT), big data, and artificial intelligence (AI), shows potential for providing athletes with continuous monitoring and in-depth analysis to support their training. This study employs wireless body area network (WBAN) and digital twin (DT) technology to design a novel system for assisting athletes training. On the hardware level, the system utilizes a WBAN with multiple sensors to collect physical and physiological data from athletes. On the software level, the system comprises three modules: motion capture, behavior recognition, and motion correction modules. These modules enable the digital twin to reflect the athlete's movements, behaviors, and physiological attributes in real-time, helping athletes understand their physical condition, correct erroneous movements, and prevent potential health hazards. Furthermore, this study demonstrates how to construct a digital twin human, providing a method that can be transplanted to other scenarios.

Recently, there has been a growing interest in the exploration of Nonlinear Matrix Decomposition (NMD) due to its close ties with neural networks. NMD aims to find a low-rank matrix from a sparse nonnegative matrix with a per-element nonlinear function. A typical choice is the Rectified Linear Unit (ReLU) activation function. To address over-fitting in the existing ReLU-based NMD model (ReLU-NMD), we propose a Tikhonov regularized ReLU-NMD model, referred to as ReLU-NMD-T. Subsequently, we introduce a momentum accelerated algorithm for handling the ReLU-NMD-T model. A distinctive feature, setting our work apart from most existing studies, is the incorporation of both positive and negative momentum parameters in our algorithm. Our numerical experiments on real-world datasets show the effectiveness of the proposed model and algorithm.

Massive multiple-input multiple-output (MIMO) has gained widespread popularity in recent years due to its ability to increase data rates, improve signal quality, and provide better coverage in challenging environments. In this paper, we investigate the MIMO beam selection (MBS) problem, which is proven to be NP-hard and computationally intractable. To deal with this problem, quantum computing that can provide faster and more efficient solutions to large-scale combinatorial optimization is considered. MBS is formulated in a quadratic unbounded binary optimization form and solved with Coherent Ising Machine (CIM) physical machine. We compare the performance of our solution with two classic heuristics, simulated annealing and Tabu search. The results demonstrate an average performance improvement by a factor of 261.23 and 20.6, respectively, which shows that CIM-based solution performs significantly better in terms of selecting the optimal subset of beams. This work shows great promise for practical 5G operation and promotes the application of quantum computing in solving computationally hard problems in communication.

The procedure of establishing the correspondence between two sets of feature points is important in computer vision applications. In this article, an elastic net constraint-based tensor model is proposed for high-order graph matching. To control the tradeoff between the sparsity and the accuracy of the matching results, an elastic net constraint is introduced into the tensor-based graph matching model. Then, a nonmonotone spectral projected gradient (NSPG) method is derived to solve the proposed matching model. During the optimization of using NSPG, we propose an algorithm to calculate the projection on the feasible convex sets of elastic net constraint. Further, the global convergence of solving the proposed model using the NSPG method was proved. The superiority of the proposed method is verified through experiments on the synthetic data and natural images.

Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters are mutually independent or Gaussian correlated, which is rarely true in real applications. For instance, in chip manufacturing, many process variations are actually correlated. Recently, some techniques have been developed to handle non-Gaussian correlated random parameters, but they are time-consuming for high-dimensional problems. We present a new framework to solve uncertainty quantification problems with many non-Gaussian correlated uncertainties. First, we propose a set of smooth basis functions to well capture the impact of non-Gaussian correlated process variations. We develop a tensor approach to compute these basis functions in a high-dimension setting. Second, we investigate the theoretical aspect and practical implementation of a sparse solver to compute the coefficients of all basis functions. We provide some theoretical analysis for the exact recovery condition and error bound of this sparse solver in the context of uncertainty quantification. We present three adaptive sampling approaches to improve the performance of the sparse solver. Finally, we validate our methods by synthetic and practical electronic/photonic ICs with 19 to 57 non-Gaussian correlated variation parameters. Our approach outperforms Monte Carlo by thousands of times in terms of efficiency. It can also accurately predict the output density functions with multiple peaks caused by non-Gaussian correlations, which are hard to capture by existing methods.

Uncertainty quantification has become an efficient tool for uncertainty-aware prediction, but its power in yield-aware optimization has not been well explored from either theoretical or application perspectives. Yield optimization is a much more challenging task. On the one side, optimizing the generally nonconvex probability measure of performance metrics is difficult. On the other side, evaluating the probability measure in each optimization iteration requires massive simulation data, especially, when the process variations are non-Gaussian correlated. This article proposes a data-efficient framework for the yield-aware optimization of photonic ICs. This framework optimizes the design performance with a yield guarantee, and it consists of two modules: 1) a modeling module that builds stochastic surrogate models for design objectives and chance constraints with a few simulation samples and 2) a novel yield optimization module that handles probabilistic objectives and chance constraints in an efficient deterministic way. This deterministic treatment avoids repeatedly evaluating probability measures at each iteration, thus it only requires a few simulations in the whole optimization flow. We validate the accuracy and efficiency of the whole framework by a synthetic example and two photonic ICs. Our optimization method can achieve more than$30\times $reduction of simulation cost and better design performance on the test cases compared with a Bayesian yield optimization approach developed recently.

Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate decision making or machine learning. In this paper, we summarize the recent applications of tensor computation in obtaining compact models for uncertainty quantification and deep learning. In uncertainty analysis where obtaining data samples is expensive, we show how tensor methods can significantly reduce the simulation or measurement cost. To enable the deployment of deep learning on resource-constrained hardware platforms, tensor methods can be used to significantly compress an over-parameterized neural network model or directly train a small-size model from scratch via optimization or statistical techniques. Recent Bayesian tensorized neural networks can automatically determine their tensor ranks in the training process.

The post-Moore era casts a shadow of uncertainty on many aspects of computer system design. Managing that uncertainty requires new algorithmic tools to make quantitative assessments. While prior uncertainty quantification methods, such as generalized polynomial chaos (gPC), show how to work precisely under the uncertainty inherent to physical devices, these approaches focus solely on variables from a continuous domain. However, as one moves up the system stack to the architecture level many parameters are constrained to a discrete (integer) domain. This paper proposes an efficient and accurate uncertainty modeling technique, named mixed generalized polynomial chaos (M-gPC), for architectural uncertainty analysis. The M-gPC technique extends the generalized polynomial chaos (gPC) theory originally developed in the uncertainty quantification community, such that it can efficiently handle the mixed-type (i.e., both continuous and discrete) uncertainties in computer architecture design. Specifically, we employ some stochastic basis functions to capture the architecture-level impact caused by uncertain parameters in a simulator. We also develop a novel mixed-integer programming method to select a small number of uncertain parameter samples for detailed simulations. With a few highly informative simulation samples, an accurate surrogate model is constructed in place of cycle-level simulators for various architectural uncertainty analysis. In the chip-multiprocessor (CMP) model, we are able to estimate the propagated uncertainties with only 95 samples whereas Monte Carlo requires$5\times 10^{4}$samples to achieve the similar accuracy. We also demonstrate the efficiency and effectiveness of our method on a detailed DRAM subsystem.

Drug repositioning, i.e., identifying new indications for known drugs, has attracted a lot of attentions recently and is becoming an effective strategy in drug development. In literature, several computational approaches have been proposed to identify potential indications of old drugs based on various types of data sources. In this paper, by formulating the drug-disease associations as a low-rank matrix, we propose a novel method, namely DrPOCS, to identify candidate indications of old drugs based on projection onto convex sets (POCS). With the integration of drug structure and disease phenotype information, DrPOCS predicts potential associations between drugs and diseases with matrix completion. Benchmarking results demonstrate that our proposed approach outperforms popular existing approaches with high accuracy. In addition, a number of novel predicted indications are validated with various types of evidences, indicating the predictive power of our proposed approach.

Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impacted many engineering fields, including variation-aware design automation of integrated circuits and integrated photonics. Due to the fast convergence rate, the generalized polynomial chaos expansion has achieved orders-of-magnitude speedup than Monte Carlo in many applications. However, almost all existing generalized polynomial chaos methods have a strong assumption: the uncertain parameters are mutually independent or Gaussian correlated. This assumption rarely holds in many realistic applications, and it has been a long-standing challenge for both theorists and practitioners.

In this paper, we study the tensor completion problem on recovery of the multilinear data under limited sampling. A popular convex relaxation of this problem is to minimize the nuclear norm of the more square matrix produced by matricizing a tensor. However, it may fail to produce a highly accurate solution under low sample ratio. In order to get a recovery with high accuracy, we propose an adaptive correction approach for tensor completion. First, a corrected model for matrix completion with bound constraint is proposed and its error bound is established. Then, we extend it to tensor completion with bound constraint and propose a corrected model for tensor completion. The adaptive correction approach consists of solving a series of corrected models with an initial estimator where the initial estimator used for the next step is computed from the value of the current solution. Moreover, the error bound of the corrected model for tensor completion is also established. A convergent 3-block alternating direction method of multipliers (ADMM) is applied to solve the dual problem of the corrected model. Numerical experiments on both random data and real world data validate the efficiency of our proposed correction approach.