Sparse time-frequency decomposition based on dictionary adaptation.

The standard traffic assignment problem (TAP) is often augmented with additional constraints to address non-standard applications. These models are called TAP with side constraints (TAPSC). Despite the rising significance of TAPSC models, the ability to efficiently solve them to satisfactory precision remains limited in real-world applications. The purpose of this paper is to fill this gap by integrating a recently developed high performance TAP solver, known as the path-based Greedy algorithm, with the augmented Lagrangian multiplier (ALM) method. This paper examines how precisely the subproblems in the ALM method should be solved to optimize the overall convergence performance. It is found that insufficiently converged subproblem solutions sometimes lead to catastrophic failures, although pursuing extremely high precision could also be counterproductive. Accordingly, it is proposed to adjust the precision required to solve the subproblems based on an approximate gap measured by the augmented Lagrangian. Results of numerical experiments show that adaptively adjusting the subproblem precision limit produces a 25% speed-up compared with the algorithm with a fixed limit.

Spatial spectral total variation has been widely used in the hyperspectral image (HSI) denoising algorithms. However, the total variation norm only penalizes the gradient magnitudes of HSIs, which may influence the recovery of denoised image edges. In this paper, we proposed a new l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> gradient regularized low-rank tensor model for removing HSI mixed noises. The low-rank tensor Tucker decomposition is applied for recovering the clean HSI part by using the HSI global correlation. The l0 gradient regularization controls the number of non-zero gradients directly and is designed to explore the spatial-spectral property of hyperspectral images and preserve important image features. The optimization problem is solved by the Augmented Lagrange Multiplier (ALM) method efficiently. The real-world data experiment demonstrates the better performance of our method.

Tensorized multi-dimensional multi-view clustering based on nonnegative matrix factorization.

Principal Component Analysis (PCA) as a tool for dimensionality reduction is widely used in many areas. In the area of bioinformatics, each involved variable corresponds to a specific gene. In order to improve the robustness of PCA-based method, this paper proposes a novel graph-Laplacian PCA algorithm by adopting L1/2 constraint (L1/2 gLPCA) on error function for feature (gene) extraction. The error function based on L1/2-norm helps to reduce the influence of outliers and noise. Augmented Lagrange Multipliers (ALM) method is applied to solve the subproblem. This method gets better results in feature extraction than other state-of-the-art PCA-based methods. Extensive experimental results on simulation data and gene expression data sets demonstrate that our method can get higher identification accuracies than others.

Speckle noise removal via nonlocal low-rank regularization

This paper presents an effective design approach for reducing the weight of a flexible rotor in ball bearings with rotational speed and load dependent stiffness characteristics under constraints on the system eigenvalues and bearing fatigue life. Design variables are chosen to be the inner radii of shaft elements, the positions of ball bearings, and the preloads on the bearings. The stiffness characteristics of high speed ball bearings are completely described as functions of applied loads and spin speed, and applied to the dynamic behavior analysis of a rotor-bearing system. A transfer matrix method is used to obtain eigenvalues of the system and an augmented Lagrange multiplier (ALM) method is employed as an optimization technique. A multi-stepped rotor supported by two angular contact ball bearings is analyzed and designed to show the speed and load dependent stiffness effect on the system dynamic behavior and to demonstrate the effectiveness of the proposed optimum design approach. The results show that the effect of the stiffness on the system dynamic behavior is noticeable and that the suggested design approach is effective. [S0739-3717(00)00803-5]

Background Subtraction (BS) is one of the key steps in video analysis. Many background models have been proposed and achieved promising performance on public data sets. However, due to challenges such as illumination change, dynamic background etc. the resulted foreground segmentation often consists of holes as well as background noise. In this regard, we consider generalized fused lasso regularization to quest for intact structured foregrounds. Together with certain assumptions about the background, such as the low-rank assumption or the sparse-composition assumption (depending on whether pure background frames are provided), we formulate BS as a matrix decomposition problem using regularization terms for both the foreground and background matrices. Moreover, under the proposed formulation, the two generally distinctive background assumptions can be solved in a unified manner. The optimization was carried out via applying the augmented Lagrange multiplier (ALM) method in such a way that a fast parametric-flow algorithm is used for updating the foreground matrix. Experimental results on several popular BS data sets demonstrate the advantage of the proposed model compared to state-of-the-arts.

The optimal economic operation of a thermal electric power production system without considering transmission losses is a critical problem for ships, aircrafts, island power systems and it is usually solved with Lagrange method. In this paper, an alternative solution method is proposed using artificial neural networks (ANN) based on augmented Lagrange multiplier method with equality and inequality constraints. The respective theoretical analysis is presented, while a specific case study is studied. The advantages and disadvantages of the method are discussed and compared with the classical Lagrange method and ANN method based on external penalty functions.

An augmented Lagrangian multiplier method based on a CHKS smoothing function for solving nonlinear bilevel programming problems

An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher &amp; Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer / discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.

Aiming at excessive users existing in a pico base station (PBS) of heterogeneous networks, the resource allocation problem of maximizing the total uplink throughput is investigated in this paper. By deploying a relay node with energy harvesting, some users of the PBS are transferred to the adjacent idle PBS. The resource allocation problem is formulated as an optimization problem. The objective is to maximize the total uplink throughput of users in the PBS under the constraints of the user's minimum data rate, the energy consumption, and transmission power of the relay node. The optimal solution is obtained by using the augmented Lagrange multiplier method. Simulation results show that the proposed method has higher throughput compared with the conventional method (i.e., some PBS users are transferred to the macro base station). Moreover, compared with the equal power method, the proposed method has an increase in terms of throughput to a certain degree.

Hilbert Huang Transform (HHT) couldn’t effectively identify voltage interruption and voltage dips. Frequency comparison method was applied to identify the two situations in this paper. The simulation results showed that the magnitude of the Intrinsic Mode Functions (IMF) components and instantaneous frequency fluctuations were not exactly the same, when the magnitude of the voltage sag was different. The magnitude of the voltage sag was larger, the average value of the amplitude of the IMF components was smaller and the instantaneous frequency fluctuations were greater. During the period of voltage interruption, the instantaneous frequency of the IMF components was almost zero and the average value of the IMF components was relatively larger. So the instantaneous frequency of voltage interruption and voltage dips different characters can help to identify the two situations and the results of the example verify to be a practicality method.

Hyperspectral video sequences (HVSs) are well suited for gas plume detection (GPD). The high spectral resolution allows the detection of chemical clouds even when they are optically thin. Processing this new type of video sequences is challenging and requires advanced image and video analysis algorithms. In this paper, we propose a novel method for GPD recorded in HVSs. Based on the assumption that the background is stationary and the gas plume is moving, the proposed method separates the background from the gas plume via a low-rank and sparse decomposition. Furthermore, taking into consideration that the gas plume is continuous in both spatial and temporal dimensions, we include total variation regularization in the constrained minimization problem, which we solve using the augmented Lagrangian multiplier method. After applying the above process to each extracted feature, a novel fusion strategy is proposed to combine the information into a final detection result. Experimental results using real data sets indicate that the proposed method achieves very promising GPD performance.

In this work, a new instantaneous fundamental frequency extraction method is presented, with the attention especially focused on its robustness for pathological voices processing. It is based on the Ensemble Empirical Mode Decomposition (EEMD) algorithm, which is a completely data-driven method for signal decomposition into a sum of AM - FM components, called Intrinsic Mode Functions (IMFs) or modes. Our results show that the speech fundamental frequency can be captured in a single IMF. We also propose an algorithm for selecting the mode where the fundamental frequency can be found, based on the logarithm of the power of the IMFs. The instantaneous frequency is then extracted by means of well-known techniques. The behaviour of the proposed method is compared with other two ones (Robust Algorithm for Pitch Tracking -RAPT- and auto-correlation based algorithms), both in normal and pathological sustained vowels.

Each year 400,000 North Americans die from sudden cardiac death (SCD). T- wave alternans (TWA) refers to an alternating pattern in the T-wave portion of the surface electrocardiogram (ECG) and has been shown as a risk stratifier for SCD. These subtle changes in the T-waves are in the micro-volt scale and ambulatory ECG recordings usually contain biological noise. Also, data non-stationarity owing to heart rate variability and the amplitude variability in TWA magnitude can limit the accuracy of the detection techniques. This necessitates the need for robust detection algorithms for processing such non-stationary data. In this thesis, we have proposed an Empirical Mode Decomposition (EMD) based scheme combined with the Instantaneous Frequency (IF). EMD decomposes the signal into several monocomponent signals called Intrinsic Mode Functions (IMFs). IF extracted from these IMFs provides an accurate estimate of time varying frequency components and hence can aid during characterization of TWAs. In order to validate the performance of the proposed detection technique, the feature vectors extracted from the IMFs were fed to a linear discriminant analysis (LDA) classifier. The performance assessment was carried out using two datasets: (a) Synthetic TWAs: 72 signals obtained from publicly accessible Physionet database and (b) TWAs from patients: 55 ambulatory ECG signals obtained from the Toronto General Hospital. Using an unbiased leave-one-out cross validation strategy, maximum overall classification accuracies of 86.1% and 81.8% were achieved for TWA detection from synthetic and ambulatory ECG recordings respectively. In addition, the usability of the proposed technique has been investigated to assess its suitability for addressing another cardiovascular problem stroke. Atrial Fibrillation (AF) has been identified as a risk factor to increase the chances of stroke. The most common method in studying the complex AF electrograms is to employ dominant frequency (DF) analysis; however, due to signal non-stationarity DF does not always provide the best estimate of the atrial activation rate. As a result, analyzing the electrograms via EMD and IF has been investigated as the second contribution of this work.