Alternating Minimization Algorithm Research Articles

Underwater Image Enhancement With Hyper-Laplacian Reflectance Priors.

Underwater image enhancement aims at improving the visibility and eliminating color distortions of underwater images degraded by light absorption and scattering in water. Recently, retinex variational models show remarkable capacity of enhancing images by estimating reflectance and illumination in a retinex decomposition course. However, ambiguous details and unnatural color still challenge the performance of retinex variational models on underwater image enhancement. To overcome these limitations, we propose a hyper-laplacian reflectance priors inspired retinex variational model to enhance underwater images. Specifically, the hyper-laplacian reflectance priors are established with the l1/2 -norm penalty on first-order and second-order gradients of the reflectance. Such priors exploit sparsity-promoting and complete-comprehensive reflectance that is used to enhance both salient structures and fine-scale details and recover the naturalness of authentic colors. Besides, the l2 norm is found to be suitable for accurately estimating the illumination. As a result, we turn a complex underwater image enhancement issue into simple subproblems that separately and simultaneously estimate the reflection and the illumination that are harnessed to enhance underwater images in a retinex variational model. We mathematically analyze and solve the optimal solution of each subproblem. In the optimization course, we develop an alternating minimization algorithm that is efficient on element-wise operations and independent of additional prior knowledge of underwater conditions. Extensive experiments demonstrate the superiority of the proposed method in both subjective results and objective assessments over existing methods. The code is available at: https://github.com/zhuangpeixian/HLRP.

Hyperspectral Image Denoising via Tensor Low-Rank Prior and Unsupervised Deep Spatial–Spectral Prior

Hyperspectral image (HSI) denoising is a fundamental task in remote sensing image processing, which is helpful for HSI subsequent applications, such as unmixing and classification. Thanks to the powerful representation ability of untrained deep neural networks, deep image prior (DIP)-based methods achieve tremendous successes in image processing (e.g., denoising and inpainting). However, DIP-based methods neglect the tensor low-rank prior of the underlying HSI which will be beneficial to capturing the global structure of the underlying HSI. To address this issue, we propose a novel model for HSI denoising, which can simultaneously take respective advantages of the tensor low-rank prior and the deep spatial-spectral prior. The tensor low-rank prior leads to a better global structure and the deep spatial-spectral prior is complementary to preserve better local details. On the one hand, we adopt low-rank tensor ring (TR) decomposition to characterize the tensor low-rank prior and capture the global structure of the underlying HSI. On the other hand, we employ untrained deep neural networks to flexibly represent the deep spatial-spectral prior and capture the local details of the underlying HSI. To solve the proposed model, we develop an efficient alternating minimization algorithm. Experimental results on simulated and real data validate the advantages of the proposed model in HSI denoising. Compared with state-of-the-art HSI denoising methods, the proposed method preserves better local details and the global structure of the underlying HSI.

Effective document image binarization via a convex variational level set model

Document image binarization is a significant stage in the optical character recognition system. Different from previous binarization approaches, in this paper, we propose a novel and convex variational level set model for document image binarization. Our energy functional is comprised of two terms: data term and fidelity term. We prove that our model is strictly convex and has a unique global minimum solution, which enables us to set the evolution termination criterion by the normalized step difference energy that measures the convergence state of level set function. We experimentally demonstrate the advantage of the fidelity term and show the merit of level set initialization robustness. In addition, the convergence of the alternative minimization algorithm for solving our model is analyzed. Extensive experiments are conducted on JM dataset, representative degraded document images and DIBCO series datasets to evaluate our model qualitatively and quantitatively. The experiment results verify that our model is effective to deal with most kinds of degraded images. Compared with four evolution and six non-evolution based binarization methods, our model could achieve better or competitive performance in terms of four metrics.

Joint Estimation of Balanced Motions and Internal Tides From Future Wide‐Swath Altimetry

AbstractWide‐swath altimetry, for example, the Surface Water and Ocean Topography mission is expected to provide Sea Surface Height (SSH) measurements resolving scales of a few tens of kilometers. Over a large fraction of the globe, the SSH signal at these scales is essentially a superposition of a component due to balanced motions (BMs) and another component due to internal tides (ITs). Several oceanographic applications require the separation of these components and their mapping on regular grids. For that purpose, the paper introduces an alternating minimization algorithm that iteratively implements two data assimilation techniques, each specific to the mapping of one component: a quasi‐geostrophic model with Back‐and‐Forth Nudging for BMs, and a linear shallow‐water model with 4‐Dimensional Variational assimilation for ITs. The algorithm is tested with Observation System Simulation Experiments where the truth is provided by a primitive‐equation ocean model in an idealized configuration simulating a turbulent jet and mode‐one ITs. The algorithm reconstructs almost 80% of the variance of BMs and ITs, the remaining 20% being mostly due to dynamics that cannot be described by the simple models used. Importantly, in addition to the reconstruction of stationary ITs, the amplitude and phase of nonstationary ITs are reconstructed. Sensitivity experiments show that the quality of reconstruction significantly depends upon the timing of observations. Although idealized, this study represents a step forward towards the disentanglement of BMs and ITs signals from real wide‐swath altimetry data.

CT Image Reconstruction via Nonlocal Low-Rank Regularization and Data-Driven Tight Frame

X-ray computed tomography (CT) is widely used in medical applications, where many efforts have been made for decades to eliminate artifacts caused by incomplete projection. In this paper, we propose a new CT image reconstruction model based on nonlocal low-rank regularity and data-driven tight frame (NLR-DDTF). Unlike the Spatial-Radon domain data-driven tight frame regularization, the proposed NLR-DDTF model uses an asymmetric treatment for image reconstruction and Radon domain inpainting, which combines the nonlocal low-rank approximation method for spatial domain CT image reconstruction and data-driven tight frame-based regularization for Radon domain image inpainting. An alternative direction minimization algorithm is designed to solve the proposed model. Several numerical experiments and comparisons are provided to illustrate the superior performance of the NLR-DDTF method.

A two-stage image reconstruction strategy for electrical impedance tomography

Electrical impedance tomography (EIT) is a potential and promising tomographic technique. Based on a reconstruction strategy, conductivity distribution can be imaged by processing boundary measurements. It should be noticed that the process of image reconstruction involves the solution of a nonlinear ill-posed inverse problem. To tackle this problem, a novel two-stage image reconstruction strategy is proposed in this work. It combines the advantages of total generalized variation regularization method and tight wavelet approach. The solution of the proposed method is acquired by employing alternating minimization algorithm and spilt Bregman algorithm. In the numerical simulation, reconstruction of five models is studied. Aside from the visual observation, we have also validated the proposed method with quantitative comparison. Meanwhile, the impact of noise on the reconstruction is considered. Furthermore, the proposed method is evaluated by phantom experimental data. The simulation and experimental results have demonstrated the superior performance of the proposed method in visualizing conductivity distribution.

Hybrid Precoding for Millimeter Wave Systems under Phase Noise problem

Millimeter wave - mm Wave - communications has been considered as a key authorised technology for the fifth generation networks. Hybrid precoding, which refer to a blend of analog and digital precoding, can achieve high spectral and energy efficiencies. However a cost-effective alternative and power consumption are needed. So hybrid precoding strategies become promising solutions. In the higher carrier frequencies, especially the millimeter-wave range, there are significant degradations in the transmitted and received signals due to radio-frequency impairments such as phase noise introduced by the local oscillators (LO), which is the irregular difference among the phase of the local oscillator and the phase of the carrier signal. It’s becoming a limiting factor in high data rate digital communication systems. In this research, we study the impact of phase noise on the performance of hybrid precoding structure in millimeter wave Multiple-Input Multiple-Output (MIMO) (mmWave MIMO) systems. Manifold optimization based alternating minimization algorithm is proposed. An optimization problem is formulated for phase noise issue in millimeter wave MIMO system. Results show that the impact of phase noise can degrade the system performance at higher RF chains.

Falsification of hybrid systems with symbolic reachability analysis and trajectory splicing

The falsification of a hybrid system aims at finding trajectories that violate a given safety property. This is a challenging problem, and the practical applicability of current falsification algorithms still suffers from their high time complexity. In contrast to falsification, verification algorithms aim at providing guarantees that no such trajectories exist. Recent symbolic reachability techniques are capable of efficiently computing linear constraints that enclose all trajectories of the system with reasonable precision. In this paper, we leverage the power of symbolic reachability algorithms to improve the scalability of falsification techniques. Recent approaches to falsification reduce the problem to a nonlinear optimization problem. We propose to reduce the search space of the optimization problem by adding linear state constraints obtained with a reachability algorithm. An empirical study of how varying abstractions during symbolic reachability analysis affect the performance of solving a falsification problem is presented. In addition, for solving a falsification problem, we propose an alternating minimization algorithm that solves a linear programming problem and a non-linear programming problem in alternation finitely many times. We showcase the efficacy of our algorithms on a number of standard hybrid systems benchmarks demonstrating the performance increase and number of falsifyable instances.

Multivariate semi-blind deconvolution of fMRI time series

Whole brain estimation of the haemodynamic response function (HRF) in functional magnetic resonance imaging (fMRI) is critical to get insight on the global status of the neurovascular coupling of an individual in healthy or pathological condition. Most of existing approaches in the literature works on task-fMRI data and relies on the experimental paradigm as a surrogate of neural activity, hence remaining inoperative on resting-stage fMRI (rs-fMRI) data. To cope with this issue, recent works have performed either a two-step analysis to detect large neural events and then characterize the HRF shape or a joint estimation of both the neural and haemodynamic components in an univariate fashion. In this work, we express the neural activity signals as a combination of piece-wise constant temporal atoms associated with sparse spatial maps and introduce an haemodynamic parcellation of the brain featuring a temporally dilated version of a given HRF model in each parcel with unknown dilation parameters. We formulate the joint estimation of the HRF shapes and spatio-temporal neural representations as a multivariate semi-blind deconvolution problem in a paradigm-free setting and introduce constraints inspired from the dictionary learning literature to ease its identifiability. A fast alternating minimization algorithm, along with its efficient implementation, is proposed and validated on both synthetic and real rs-fMRI data at the subject level. To demonstrate its significance at the population level, we apply this new framework to the UK Biobank data set, first for the discrimination of haemodynamic territories between balanced groups (n=24 individuals in each) patients with an history of stroke and healthy controls and second, for the analysis of normal aging on the neurovascular coupling. Overall, we statistically demonstrate that a pathology like stroke or a condition like normal brain aging induce longer haemodynamic delays in certain brain areas (e.g. Willis polygon, occipital, temporal and frontal cortices) and that this haemodynamic feature may be predictive with an accuracy of 74 % of the individual’s age in a supervised classification task performed on n=459 subjects.

Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold

Data-driven computing in elasticity attempts to directly use experimental data on material, without constructing an empirical model of the constitutive relation, to predict an equilibrium state of a structure subjected to a specified external load. Provided that a data set comprising stress–strain pairs of material is available, a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie (Kanno 2021, Jpn. J. Ind. Appl. Math.). From the perspective of physical experiments, stress field cannot be directly measured, while displacement and force fields are measurable. In this study, we extend the previous kernel method to the situation that pairs of displacement and force, instead of pairs of stress and strain, are available as an input data set. A new regularized least-squares problem is formulated in this problem setting, and an alternating minimization algorithm is proposed to solve the problem.

Unifying tensor factorization and tensor nuclear norm approaches for low-rank tensor completion

Low-rank tensor completion (LRTC) has gained significant attention due to its powerful capability of recovering missing entries. However, it has to repeatedly calculate the time-consuming singular value decomposition (SVD). To address this drawback, we, based on the tensor-tensor product (t-product), propose a new LRTC method-the unified tensor factorization (UTF)-for 3-way tensor completion. We first integrate the tensor factorization (TF) and the tensor nuclear norm (TNN) regularization into a framework that inherits the benefits of both TF and TNN: fast calculation and convex optimization. The conditions under which TF and TNN are equivalent are analyzed. Then, UTF for tensor completion is presented and an efficient iterative updated algorithm based on the alternate direction method of multipliers (ADMM) is used for our UTF optimization, and the solution of the proposed alternate minimization algorithm is also proven to be able to converge to a Karush–Kuhn–Tucker (KKT) point. Finally, numerical experiments on synthetic data completion and image/video inpainting tasks demonstrate the effectiveness of our method over other state-of-the-art tensor completion methods.

Iterative reconstruction for low-dose cerebral perfusion computed tomography using prior image induced diffusion tensor

Cerebral perfusion computed tomography (CPCT) can depict the functional status of cerebral circulation at the tissue level; hence, it has been increasingly used to diagnose patients with cerebrovascular disease. However, there is a significant concern that CPCT scanning protocol could expose patients to excessive radiation doses. Although reducing the x-ray tube current when acquiring CPCT projection data is an effective method for reducing radiation dose, this technique usually results in degraded image quality. To enhance the image quality of low-dose CPCT, we present a prior image induced diffusion tensor (PIDT) for statistical iterative reconstruction, based on the penalized weighted least-squares (PWLS) criterion, which we referred to as PWLS-PIDT, for simplicity. Specifically, PIDT utilizes the geometric features of pre-contrast scanned high-quality CT image as a structure prior for PWLS reconstruction; therefore, the low-dose CPCT images are enhanced while preserving important features in the target image. An effective alternating minimization algorithm is developed to solve the associated objective function in the PWLS-PIDT reconstruction. We conduct qualitative and quantitative studies to evaluate the PWLS-PIDT reconstruction with a digital brain perfusion phantom and patient data. With this method, the noise in the reconstructed CPCT images is more substantially reduced than that of other competing methods, without sacrificing structural details significantly. Furthermore, the CPCT sequential images reconstructed via the PWLS-PIDT method can derive more accurate hemodynamic parameter maps than those of other competing methods.

Product demand estimation for vending machines using video surveillance data: A group-lasso method

Lost sales information has significant impacts on the estimation of product demand and substitution. However, the difficulties to recognize such information in real applications make it rarely used in research. In this paper, we come up with a novel group-lasso based product demand model using the lost sales information, which is extracted from the video surveillance data provided by the cooperate retailer. A group-lasso method is used to characterize the substitution behaviours among each pair of SKUs. Then, an alternating minimization algorithm whose efficiency and convergence have been proved is designed to solve the model. To evaluate the model, we provide comparative experiments between the proposed method, time series forecasting and a naive method by applying these models to a real data set. The experiment results show that the proposed model obtains 8% higher accuracy at the total sales level and forecasts more accurately at the SKU sales level as well, which demonstrate its superiority. Moreover, we define a pair of welfare functions to measure the social impacts from both the retailer’s and customer’s end.

Second-order total generalized variation based model for restoring images with mixed Poisson — Gaussian noise

Introduction: A common problem in image restoration is image denoising. Among many noise models, the mixed Poisson-Gaussian model has recently aroused considerable interest. Purpose: Development of a model for denoising images corrupted by mixed Poisson-Gaussian noise, along with an algorithm for solving the resulting minimization problem. Results: We proposed a new total variation model for restoring an image with mixed Poisson-Gaussian noise, based on second-order total generalized variation. In order to solve this problem, an efficient alternating minimization algorithm is used. To illustrate its comparison with related methods, experimental results are presented, demonstrating the high efficiency of the proposed approach. Practical relevance: The proposed model allows you to remove mixed Poisson-Gaussian noise in digital images, preserving the edges. The presented numerical results demonstrate the competitive features of the proposed model.

Blind deconvolution using bilateral total variation regularization: a theoretical study and application

ABSTRACT Blind image deconvolution recovers a deblurred image and the blur kernel from a blurred image. From a mathematical point of view, this is a strongly ill-posed problem and several works have been proposed to address it. One successful approach proposed by Chan and Wong consists in using the total variation (TV) as a regularization for both the image and the kernel. These authors also introduced an Alternating Minimization (AM) algorithm in order to compute a physical solution. Unfortunately, Chan's approach suffers in particular from the ringing and staircasing effects produced by the TV regularization. To address these problems, we propose a new model based on Bilateral Total Variation (BTV) regularization of the image keeping the same regularization for the kernel. We prove the existence of a minimizer of a proposed variational problem in a suitable space using a relaxation process. We also propose an AM algorithm based on our model. The efficiency and robustness of our model are illustrated and compared with the TV method through numerical simulations.

Multirobot Collaborative Monocular SLAM Utilizing Rendezvous

Multirobot simultaneous localization and mapping (SLAM) requires technical ingredients such as systematic construction of multiple SLAM systems and collection of information from each robot. In particular, map fusion is an essential process of multirobot SLAM that combines multiple local maps estimated by team robots into a global map. Fusion of multiple local maps is usually based on interloop detection that recognizes the same scene visited by multiple robots, or robot rendezvous where a member(s) of a robot team is observed in another member's images. This article proposes a collaborative monocular SLAM including a map fusion algorithm that utilizes rendezvous, which can happen when multirobot team members operate in close proximity. Unlike existing rendezvous-based approaches that require additional sensors, the proposed system uses a monocular camera only. Our system can recognize robot rendezvous using nonstatic features (NSFs) without fiducial markers to identify team robots. NSFs, which are abandoned as outliers in typical SLAM systems for not supporting ego-motion, can include relative bearing measurements between robots in a rendezvous situation. The proposed pipeline consists of the following: first, a feature identification module that extracts the relative bearing measurements between robots from NSFs consisting of anonymous bearing vectors with false positives, and second, a map fusion module that integrates the map from the observer robot with the maps from the observed robots using identified relative measurements. The feature identification module can operate quickly using the proposed alternating minimization algorithm formulated by two subproblems with closed-form solutions. The experimental results confirm that our collaborative monocular SLAM system recognizes rendezvous rapidly and robustly, and fuses local maps of team robots into a global map accurately.

Ranking recovery from limited pairwise comparisons using low-rank matrix completion

This paper proposes a new methodology for solving the well-known rank aggregation problem from pairwise comparisons using low-rank matrix completion. Partial and noisy data of pairwise comparisons is first transformed into a matrix form. We then use tools from matrix completion, which has served as a major component in the low-rank based completion solution for the Netflix challenge, to construct the preference of different objects. In our approach, the data from multiple comparisons is used to create an estimate of the probability of object i winning (or be chosen) over object j, where only a partial set of comparisons between the N objects is known. These probabilities can be transformed to take the form of a rank-one matrix. An alternating minimization algorithm, in which the target matrix takes a bilinear form, is used in combination with maximum likelihood estimation for both factors. The reconstructed matrix is used to obtain the true underlying preference intensity. We start by exploring the asymptotic case of an infinitely large number of comparisons (“noiseless case”). We then extend our solution to the case of a finite number of comparisons for a subset of pairs (“noisy case”). This work demonstrates the improvement of our proposed algorithm over the state-of-the-art techniques in both simulated scenarios and real data.

Initial Value Acceleration-Based Alternating Minimization Algorithm for Dynamic Sub-Connected Hybrid Precoding in Millimeter Wave MIMO Systems

Symmetry-based sub-connected hybrid precoding is an energy-friendly structure in wireless communications. Most of the prior work set a diagonal constraint on the analog precoder and used a randomly set matrix as the initial analog precoder, which did not match the optimal channel conditions, leading to a decrease in spectral efficiency, and some had huge complexity when calculating the digital precoder. Aiming to solve these problems, this paper proposed a low-complexity hybrid precoding algorithm based on Initial value Acceleration-based Alternating Minimization (IAAM). Leveraging the special structure of analog precoder in sub-connected scheme, we design the analog precoder through low-complexity quadratic programming and use the least square method to obtain the digital precoder. Moreover, we design a heuristic algorithm with the objective function of maximizing the effective channel gain to calculate the initial analog precoder as the starting point for alternating minimization. The simulation results show that the spectral efficiency of this algorithm is at least 17.5% higher than the existing two traditional sub-connected algorithms. Additionally, it increases energy efficiency by at least 12.8% compa with the Orthogonal Matching Pursuit (OMP) algorithm. Its algorithm convergence speed is fast, which increases with the number of RF chains.

Nonisometric Surface Registration via Conformal Laplace–Beltrami Basis Pursuit

Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are nearly isometric. However, it is much more challenging to compute correspondence between surfaces which are intrinsically less similar. In this paper, we propose a variational model to align the Laplace-Beltrami (LB) eigensytems of two non-isometric genus zero shapes via conformal deformations. This method enables us to compute geometrically meaningful point-to-point maps between non-isometric shapes. Our model is based on a novel basis pursuit scheme whereby we simultaneously compute a conformal deformation of a ’target shape’ and its deformed LB eigensystem. We solve the model using a proximal alternating minimization algorithm hybridized with the augmented Lagrangian method which produces accurate correspondences given only a few landmark points. We also propose a re-initialization scheme to overcome some of the difficulties caused by the non-convexity of the variational problem. Intensive numerical experiments illustrate the effectiveness and robustness of the proposed method to handle non-isometric surfaces with large deformation with respect to both noises on the underlying manifolds and errors within the given landmarks or feature functions.

Extended Gauss-Newton and ADMM-Gauss-Newton algorithms for low-rank matrix optimization

In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle general smooth convex objective function. We show, under mild conditions, that the proposed algorithm globally and locally converges to a stationary point of the original problem. We also show empirically that the GN algorithm achieves higher accurate solutions than the alternating minimization algorithm (AMA). Then, we specify our GN scheme to handle the symmetric case and prove its convergence, where AMA is not applicable. Next, we incorporate our GN scheme into the alternating direction method of multipliers (ADMM) to develop an ADMM-GN algorithm. We prove that, under mild conditions and a proper choice of the penalty parameter, our ADMM-GN globally converges to a stationary point of the original problem. Finally, we provide several numerical experiments to illustrate the proposed algorithms. Our results show that the new algorithms have encouraging performance compared to existing methods.