Yaming Wang

Sparsity-constrained SENSE reconstruction: an efficient implementation using a fast composite splitting algorithm.

Parallel imaging and compressed sensing have been arguably the most successful and widely used techniques for fast magnetic resonance imaging (MRI). Recent studies have shown that the combination of these two techniques is useful for solving the inverse problem of recovering the image from highly under-sampled k-space data. In sparsity-enforced sensitivity encoding (SENSE) reconstruction, the optimization problem involves data fidelity (L2-norm) constraint and a number of L1-norm regularization terms (i.e. total variation or TV, and L1 norm). This makes the optimization problem difficult to solve due to the non-smooth nature of the regularization terms. In this paper, to effectively solve the sparsity-regularized SENSE reconstruction, we utilize a new optimization method, called fast composite splitting algorithm (FCSA), which was developed for compressed sensing MRI. By using a combination of variable splitting and operator splitting techniques, the FCSA algorithm decouples the large optimization problem into TV and L1 sub-problems, which are then, solved efficiently using existing fast methods. The operator splitting separates the smooth terms from the non-smooth terms, so that both terms are treated in an efficient manner. The final solution to the SENSE reconstruction is obtained by weighted solutions to the sub-problems through an iterative optimization procedure. The FCSA-based parallel MRI technique is tested on MR brain image reconstructions at various acceleration rates and with different sampling trajectories. The results indicate that, for sparsity-regularized SENSE reconstruction, the FCSA-based method is capable of achieving significant improvements in reconstruction accuracy when compared with the state-of-the-art reconstruction method.

Application of kernel principal component analysis and support vector regression for reconstruction of cardiac transmembrane potentials.

Non-invasively reconstructing the transmembrane potentials (TMPs) from body surface potentials (BSPs) constitutes one form of the inverse ECG problem that can be treated as a regression problem with multi-inputs and multi-outputs, and which can be solved using the support vector regression (SVR) method. In developing an effective SVR model, feature extraction is an important task for pre-processing the original input data. This paper proposes the application of principal component analysis (PCA) and kernel principal component analysis (KPCA) to the SVR method for feature extraction. Also, the genetic algorithm and simplex optimization method is invoked to determine the hyper-parameters of the SVR. Based on the realistic heart-torso model, the equivalent double-layer source method is applied to generate the data set for training and testing the SVR model. The experimental results show that the SVR method with feature extraction (PCA-SVR and KPCA-SVR) can perform better than that without the extract feature extraction (single SVR) in terms of the reconstruction of the TMPs on epi- and endocardial surfaces. Moreover, compared with the PCA-SVR, the KPCA-SVR features good approximation and generalization ability when reconstructing the TMPs.

Study on Parameter Optimization for Support Vector Regression in Solving the Inverse ECG Problem

The typical inverse ECG problem is to noninvasively reconstruct the transmembrane potentials (TMPs) from body surface potentials (BSPs). In the study, the inverse ECG problem can be treated as a regression problem with multi-inputs (body surface potentials) and multi-outputs (transmembrane potentials), which can be solved by the support vector regression (SVR) method. In order to obtain an effective SVR model with optimal regression accuracy and generalization performance, the hyperparameters of SVR must be set carefully. Three different optimization methods, that is, genetic algorithm (GA), differential evolution (DE) algorithm, and particle swarm optimization (PSO), are proposed to determine optimal hyperparameters of the SVR model. In this paper, we attempt to investigate which one is the most effective way in reconstructing the cardiac TMPs from BSPs, and a full comparison of their performances is also provided. The experimental results show that these three optimization methods are well performed in finding the proper parameters of SVR and can yield good generalization performance in solving the inverse ECG problem. Moreover, compared with DE and GA, PSO algorithm is more efficient in parameters optimization and performs better in solving the inverse ECG problem, leading to a more accurate reconstruction of the TMPs.

Analysis of wavelet basis selection in optimal trajectory space finding for 3D non-rigid structure from motion

Trajectory representation model has been proposed to describe non-rigid deformation. An optimal trajectory space finding algorithm for 3D non-rigid structure from motion (OTSF-NRSFM) based on this model also has been proposed. However, the influence of the wavelet basis selection on the OTSF-NRSFM algorithm has still not been studied. To help OTSF-NRSFM researchers select wavelet basis properly, we investigated the influences of wavelet basis selection. Two typical wavelet bases, DCT basis and WHT basis, are discussed in this paper. The spectrum properties of wavelet basis and feature point trajectory, trajectory representation results on synthetic shark data, OTSF-NRSFM reconstruction results on synthetic data and real data are analyzed. The results show that the wavelet selection has much influence on OTSF-NRSFM reconstruction results of some non-rigid feature points, which have complicated trajectory. This paper gives researchers some inspiration about wavelet basis selection in OTSF-NRSFM algorithm.

Non-Rigid Structure Estimation in Trajectory Space from Monocular Vision

In this paper, the problem of non-rigid structure estimation in trajectory space from monocular vision is investigated. Similar to the Point Trajectory Approach (PTA), based on characteristic points’ trajectories described by a predefined Discrete Cosine Transform (DCT) basis, the structure matrix was also calculated by using a factorization method. To further optimize the non-rigid structure estimation from monocular vision, the rank minimization problem about structure matrix is proposed to implement the non-rigid structure estimation by introducing the basic low-rank condition. Moreover, the Accelerated Proximal Gradient (APG) algorithm is proposed to solve the rank minimization problem, and the initial structure matrix calculated by the PTA method is optimized. The APG algorithm can converge to efficient solutions quickly and lessen the reconstruction error obviously. The reconstruction results of real image sequences indicate that the proposed approach runs reliably, and effectively improves the accuracy of non-rigid structure estimation from monocular vision.

A Hybrid Model of Maximum Margin Clustering Method and Support Vector Regression for Noninvasive Electrocardiographic Imaging

Noninvasive electrocardiographic imaging, such as the reconstruction of myocardial transmembrane potentials (TMPs) distribution, can provide more detailed and complicated electrophysiological information than the body surface potentials (BSPs). However, the noninvasive reconstruction of the TMPs from BSPs is a typical inverse problem. In this study, this inverse ECG problem is treated as a regression problem with multi-inputs (BSPs) and multioutputs (TMPs), which will be solved by the Maximum Margin Clustering- (MMC-) Support Vector Regression (SVR) method. First, the MMC approach is adopted to cluster the training samples (a series of time instant BSPs), and the individual SVR model for each cluster is then constructed. For each testing sample, we find its matched cluster and then use the corresponding SVR model to reconstruct the TMPs. Using testing samples, it is found that the reconstructed TMPs results with the MMC-SVR method are more accurate than those of the single SVR method. In addition to the improved accuracy in solving the inverse ECG problem, the MMC-SVR method divides the training samples into clusters of small sample sizes, which can enhance the computation efficiency of training the SVR model.

Sparse approximation for nonrigid structure from motion

This paper introduces applying a novel sparse approximation method into solving nonrigid structure from motion problem in trajectory space. Instead of generating a truncated traditional trajectory basis, this method uses an atom dictionary which includes a set of overcomplete bases to estimate the real shape of the deformable object. Yet, it still runs reliably and can get an optimal result. On the other hand, it does not need to consider the size of predefined trajectory bases; that is to say, there is no need to truncate the trajectory basis. The mentioned method is very easy to implement and the only trouble which needs to be solved is an L1-regularized least squares problem. This paper not only presents a new thought, but also gives out a simple but effective solution for the nonrigid structure from motion problem.

The combination of self-organizing feature maps and support vector regression for solving the inverse ECG problem

Noninvasive electrical imaging of the heart aims to quantitatively reconstruct transmembrane potentials (TMPs) from body surface potentials (BSPs), which is a typical inverse problem. Classically, electrocardiography (ECG) inverse problem is solved by regularization techniques. In this study, it is treated as a regression problem with multi-inputs (BSPs) and multi-outputs (TMPs). Then the resultant regression problem is solved by a hybrid method, which combines the support vector regression (SVR) method with self-organizing feature map (SOFM) techniques. The hybrid SOFM-SVR method conducts a two-step process: SOFM algorithm is used to cluster the training samples and the individual SVR method is employed to construct the regression model. For each testing sample, the cluster operation can effectively improve the efficiency of the regression algorithm, and also helps the setup of the corresponding SVR model for the TMPs reconstruction. The performance of the developed SOFM-SVR model is tested using our previously developed realistic heart-torso model. The experiment results show that, compared with traditional single SVR method in solving the inverse ECG problem, the proposed method can reduce the cost of training time and improve the reconstruction accuracy in solving the inverse ECG problem.

3-D human motion estimation using regularization with 2-D feature point tracking

A novel approach is proposed to 3-D human motion estimation using regularization. First, a method of feature point tracking is developed based on /spl alpha/-/spl beta/ filter and genetic algorithm. The outliers and occluded points can be solved by this method. Then, in order to deal with the ill-posed estimation problem, a regularization approach is proposed, which is based on the results of 2-D feature point tracking and the motion smoothness between consecutive estimation groups. Thus, the ill-posed problem is converted to a well-posed one. Experimental results also demonstrate the feasibility of the proposed approach.

Noninvasive reconstruction of cardiac transmembrane potentials using a kernelized extreme learning method.

Non-invasively reconstructing the cardiac transmembrane potentials (TMPs) from body surface potentials can act as a regression problem. The support vector regression (SVR) method is often used to solve the regression problem, however the computational complexity of the SVR training algorithm is usually intensive. In this paper, another learning algorithm, termed as extreme learning machine (ELM), is proposed to reconstruct the cardiac transmembrane potentials. Moreover, ELM can be extended to single-hidden layer feed forward neural networks with kernel matrix (kernelized ELM), which can achieve a good generalization performance at a fast learning speed. Based on the realistic heart-torso models, a normal and two abnormal ventricular activation cases are applied for training and testing the regression model. The experimental results show that the ELM method can perform a better regression ability than the single SVR method in terms of the TMPs reconstruction accuracy and reconstruction speed. Moreover, compared with the ELM method, the kernelized ELM method features a good approximation and generalization ability when reconstructing the TMPs.