Regularized common spatial pattern with aggregation for EEG classification in small-sample setting

Common spatial pattern (CSP) is a popular algorithm for classifying electroencephalogram (EEG) signals in the context of brain-computer interfaces (BCIs). This paper presents a regularization and aggregation technique for CSP in a small-sample setting (SSS). Conventional CSP is based on a sample-based covariance-matrix estimation. Hence, its performance in EEG classification deteriorates if the number of training samples is small. To address this concern, a regularized CSP (R-CSP) algorithm is proposed, where the covariance-matrix estimation is regularized by two parameters to lower the estimation variance while reducing the estimation bias. To tackle the problem of regularization parameter determination, R-CSP with aggregation (R-CSP-A) is further proposed, where a number of R-CSPs are aggregated to give an ensemble-based solution. The proposed algorithm is evaluated on data set IVa of BCI Competition III against four other competing algorithms. Experiments show that R-CSP-A significantly outperforms the other methods in average classification performance in three sets of experiments across various testing scenarios, with particular superiority in SSS.     

Single frequency inverse obstacle scattering: a sparsity constrained linear sampling method approach

The linear sampling method (LSM) offers a qualitative image reconstruction approach, which is known as a viable alternative for obstacle support identification to the well-studied filtered backprojection (FBP), which depends on a linearized forward scattering model. Of practical interest is the imaging of obstacles from sparse aperture far-field data under a fixed single frequency mode of operation. Under this scenario, the Tikhonov regularization typically applied to LSM produces poor images that fail to capture the obstacle boundary. In this paper, we employ an alternative regularization strategy based on constraining the sparsity of the solution's spatial gradient. Two regularization approaches based on the spatial gradient are developed. A numerical comparison to the FBP demonstrates that the new method's ability to account for aspect-dependent scattering permits more accurate reconstruction of concave obstacles, whereas a comparison to Tikhonov-regularized LSM demonstrates that the proposed approach significantly improves obstacle recovery with sparse-aperture data.     

Multiclass common spatial patterns and information theoretic feature extraction

We address two shortcomings of the common spatial patterns (CSP) algorithm for spatial filtering in the context of brain--computer interfaces (BCIs) based on electroencephalography/magnetoencephalography (EEG/MEG): First, the question of optimality of CSP in terms of the minimal achievable classification error remains unsolved. Second, CSP has been initially proposed for two-class paradigms. Extensions to multiclass paradigms have been suggested, but are based on heuristics. We address these shortcomings in the framework of information theoretic feature extraction (ITFE). We show that for two-class paradigms, CSP maximizes an approximation of mutual information of extracted EEG/MEG components and class labels. This establishes a link between CSP and the minimal classification error. For multiclass paradigms, we point out that CSP by joint approximate diagonalization (JAD) is equivalent to independent component analysis (ICA), and provide a method to choose those independent components (ICs) that approximately maximize mutual information of ICs and class labels. This eliminates the need for heuristics in multiclass CSP, and allows incorporating prior class probabilities. The proposed method is applied to the dataset IIIa of the third BCI competition, and is shown to increase the mean classification accuracy by 23.4% in comparison to multiclass CSP.     

Common Spatial Pattern Ensemble Classifier and Its Application in Brain-Computer Interface

Common spatial pattern (CSP) algorithm is a successful tool in feature estimate of brain-computer interface (BCI). However, CSP is sensitive to outlier and may result in poor outcomes since it is based on pooling the covariance matrices of trials. In this paper, we propose a simple yet effective approach, named common spatial pattern ensemble (CSPE) classifier, to improve CSP performance. Through division of recording channels, multiple CSP filters are constructed. By projection, log-operation, and subtraction on the original signal, an ensemble classifier, majority voting, is achieved and outlier contaminations are alleviated. Experiment results demonstrate that the proposed CSPE classifier is robust to various artifacts and can achieve an average accuracy of 83.02%.     

Common Spatial Pattern Ensemble Classifier and Its Application in Brain-Computer Interface

Abstract-Common spatial pattern （CSP） algorithm is a successful tool in feature estimate of brain-computer interface （BCI）. However, CSP is sensitive to outlier and may result in poor outcomes since it is based on pooling the covariance matrices of trials. In this paper, we propose a simple yet effective approach, named common spatial pattern ensemble （CSPE） classifier, to improve CSP performance. Through division of recording channels, multiple CSP filters are constructed. By projection, log-operation, and subtraction on the original signal, an ensemble classifier, majority voting, is achieved and outlier contaminations are alleviated. Experiment results demonstrate that the proposed CSPE classifier is robust to various artifacts and can achieve an average accuracy of 83.02%.     

Data fusion: color edge detection and surface reconstructionthrough regularization

Data fusion provides tools for solving problems which are characterized by distributed and diverse information sources. In this paper, the authors focus on the problem of extracting features such as image discontinuities from both synthetic and real images. Since edge detection and surface reconstruction are ill-posed problems in the sense of Hadamard, Tikhonov's regularization paradigm is proposed as the basic tool for solving this inversion problem and restoring well-posedness. The proposed framework includes: (1) a systematic view of oneand two-dimensional regularization; (2) extension of the standard Tikhonov regularization method by allowing space-variant regularization parameters; and (3) further extension of the regularization paradigm by adding multiple data sources to allow for data fusion. The theoretical approach is complemented by developing a series of algorithms, then solving the early vision problems of color edge detection and surface reconstruction. An evaluation of these methods reveals that this new analytical data fusion technique output is consistently better than each of the individual RGB edge maps, and noisy corrupted images are reconstructed into smooth noiseless surfaces     

An Algorithm for Idle-State Detection and Continuous Classifier Design in Motor-Imagery-Based BCI

Abstract-The development of asynchronous brain-computer interface （BCI） based on motor imagery （M1） poses the research in algorithms for detecting the nontask states （i.e., idle state） and the design of continuous classifiers that classify continuously incoming electroencephalogram （EEG） samples. An algorithm is proposed in this paper which integrates two two-class classifiers to detect idle state and utilizes a sliding window to achieve continuous outputs. The common spatial pattern （CSP） algorithm is used to extract features of EEG signals and the linear support vector machine （SVM） is utilized to serve as classifier. The algorithm is applied on dataset IVb of BCI competition Ⅲ, with a resulting mean square error of 0.66. The result indicates that the proposed algorithm is feasible in the first step of the development of asynchronous systems.     

Combining spatial filters for the classification of single-trial EEG in a finger movement task

Brain-computer interface (BCI) is to provide a communication channel that translates human intention reflected by a brain signal such as electroencephalogram (EEG) into a control signal for an output device. In recent years, the event-related desynchronization (ERD) and movement-related potentials (MRPs) are utilized as important features in motor related BCI system, and the common spatial patterns (CSP) algorithm has shown to be very useful for ERD-based classification. However, as MRPs are slow nonoscillatory EEG potential shifts, CSP is not an appropriate approach for MRPs-based classification. Here, another spatial filtering algorithm, discriminative spatial patterns (DSP), is newly introduced for better extraction of the difference in the amplitudes of MRPs, and it is integrated with CSP to extract the features from the EEG signals recorded during voluntary left versus right finger movement tasks. A support vector machines (SVM) based framework is designed as the classifier for the features. The results show that, for MRPs and ERD features, the combined spatial filters can realize the single-trial EEG classification better than anyone of DSP and CSP alone does. Thus, we propose an EEG-based BCI system with the two feature sets, one based on CSP (ERD) and the other based on DSP (MRPs), classified by SVM.     

An Algorithm for Idle-State Detection and Continuous Classifier Design in Motor-Imagery-Based BCI

The development of asynchronous braincomputer interface (BCI) based on motor imagery (MI) poses the research in algorithms for detecting the nontask states (i.e., idle state) and the design of continuous classifiers that classify continuously incoming electroencephalogram (EEG) samples. An algorithm is proposed in this paper which integrates two two-class classifiers to detect idle state and utilizes a sliding window to achieve continuous outputs. The common spatial pattern (CSP) algorithm is used to extract features of EEG signals and the linear support vector machine (SVM) is utilized to serve as classifier. The algorithm is applied on dataset IVb of BCI competition III, with a resulting mean square error of 0.66. The result indicates that the proposed algorithm is feasible in the first step of the development of asynchronous systems.     

L1-norm-based common spatial patterns

Common spatial patterns (CSP) is a commonly used method of spatial filtering for multichannel electroencephalogram (EEG) signals. The formulation of the CSP criterion is based on variance using L2-norm, which implies that CSP is sensitive to outliers. In this paper, we propose a robust version of CSP, called CSP-L1, by maximizing the ratio of filtered dispersion of one class to the other class, both of which are formulated by using L1-norm rather than L2-norm. The spatial filters of CSP-L1 are obtained by introducing an iterative algorithm, which is easy to implement and is theoretically justified. CSP-L1 is robust to outliers. Experiment results on a toy example and datasets of BCI competitions demonstrate the efficacy of the proposed method.     

Analysis of Resolution and Noise Properties of Nonquadratically Regularized Image Reconstruction Methods for PET

We present accurate and efficient methods for estimating the spatial resolution and noise properties of nonquadratically regularized image reconstruction for positron emission tomography (PET). It is well known that quadratic regularization tends to over-smooth sharp edges. Many types of edge-preserving nonquadratic penalties have been proposed to overcome this problem. However, there has been little research on the quantitative analysis of nonquadratic regularization due to its nonlinearity. In contrast, quadratically regularized estimators are approximately linear and are well understood in terms of resolution and variance properties. We derive new approximate expressions for the linearized local perturbation response (LLPR) and variance using the Taylor expansion with the remainder term. Although the expressions are implicit, we can use them to accurately predict resolution and variance for nonquadratic regularization where the conventional expressions based on the first-order Taylor truncation fail. They also motivate us to extend the use of a certainty-based modified penalty to nonquadratic regularization cases in order to achieve spatially uniform perturbation responses, analogous to uniform spatial resolution in quadratic regularization. Finally, we develop computationally efficient methods for predicting resolution and variance of nonquadratically regularized reconstruction and present simulations that illustrate the validity of these methods.     

脑-机接口中基于ERS/ERD的自适应空间滤波算法

在与运动相关的脑-机接口(Brain-Computer Interface,BCI)研究中,如果样本规模小,共同空间模式(Common Spatial Patterns,CSP)滤波算法对离群点(可能为噪声)敏感,鲁棒性不好.为此该文提出自适应空间滤波(Adaptive Spatial Filter,ASF)算法,抽取滤波后脑电信号的方差作为特征,并寻找最优滤波器使两类特征中心的比值最大.与CSP不同,ASF是迭代算法,具有软判决机制,能够依据历代更新后的滤波器,自适应地降低离群点对各类特征中心计算带来的影响.采用BCI competition 2003和2005中两套数据集进行实验,结果表明:尤其是在训练样本少的情况下,相对于CSP,ASF所提取的特征分类效果更好.     

Parallel MR image reconstruction using augmented Lagrangian methods

Magnetic resonance image (MRI) reconstruction using SENSitivity Encoding (SENSE) requires regularization to suppress noise and aliasing effects. Edge-preserving and sparsity-based regularization criteria can improve image quality, but they demand computation-intensive nonlinear optimization. In this paper, we present novel methods for regularized MRI reconstruction from undersampled sensitivity encoded data--SENSE-reconstruction--using the augmented Lagrangian (AL) framework for solving large-scale constrained optimization problems. We first formulate regularized SENSE-reconstruction as an unconstrained optimization task and then convert it to a set of (equivalent) constrained problems using variable splitting. We then attack these constrained versions in an AL framework using an alternating minimization method, leading to algorithms that can be implemented easily. The proposed methods are applicable to a general class of regularizers that includes popular edge-preserving (e.g., total-variation) and sparsity-promoting (e.g., l(1)-norm of wavelet coefficients) criteria and combinations thereof. Numerical experiments with synthetic and in vivo human data illustrate that the proposed AL algorithms converge faster than both general-purpose optimization algorithms such as nonlinear conjugate gradient (NCG) and state-of-the-art MFISTA.     

Transfer Learning of BCI Using CUR Algorithm

The brain computer interface (BCI) are used in many applications including medical, environment, education, economy, and social fields. In order to have a high performing BCI classification, the training set must contain variations of high quality subjects which are discriminative. Variations will also drive transferability of training data for generalization purposes. However, if the test subject is unique from the training set variations, BCI performance may suffer. Previously, this problem was solved by introducing transfer learning in the context of spatial filtering on small training set by creating high quality variations within training subjects. In this study however, it was discovered that transfer learning can also be used to compress the training data into an optimal compact size while improving training data performance. The transfer learning framework proposed was on motor imagery BCI-EEG using CUR matrix decomposition algorithm which decomposes data into two components; C and UR which is each subject’s EEG signal and common matrix derived from historical EEG data, respectively. The method is considered transfer learning process because it utilizes historical data as common matrix for the classification purposes. This framework is implemented in the BCI system along with Common Spatial Pattern (CSP) as features extractor and Extreme Learning Machine (ELM) as classifier and this combination exhibits an increase of accuracy to up to 26% with 83% training database compression.

     

Recognition of motor imagery tasks for BCI using CSP and chaotic PSO twin SVM

Accurate modeling and recognition of the brain activity patterns for reliable communication and interaction are still a challenging task for the motor imagery (MI) brain-computer interface (BCI) system. In this paper, we propose a common spatial pattern (CSP) and chaotic particle swarm optimization (CPSO) twin support vector machine (TWSVM) scheme for classification of MI electroencephalography (EEG). The self-adaptive artifact removal and CSP were used to obtain the most distinguishable features. To improve the recognition results, CPSO was employed to tune the hyper-parameters of the TWSVM classifier. The usefulness of the proposed method was evaluated using the BCI competition IV-IIa dataset. The experimental results showed that the mean recognition accuracy of our proposed method was increased by 5.35%, 4.33%, 0.78%, 1.45%, and 9.26% compared with the CPSO support vector machine (SVM), particle swarm optimization (PSO) TWSVM, linear discriminant analysis LDA), back propagation (BP) and probabilistic neural network (PNN), respectively. Furthermore, it achieved a faster or comparable central processing unit (CPU) running time over the traditional SVM methods.     

Regularized reconstruction in electrical impedance tomography usinga variance uniformization constraint

This paper describes a new approach to reconstruction of the conductivity field in electrical impedance tomography. Our goal is to improve the tradeoff between the quality of the images and the numerical complexity of the reconstruction method. In order to reduce the computational load, we adopt a linearized approximation to the forward problem that describes the relationship between the unknown conductivity and the measurements. In this framework, we focus on finding a proper way to cope with the ill-posed nature of the problem, mainly caused by strong attenuation phenomena; this is done by devising regularization techniques well suited to this particular problem. First, we propose a solution which is based on Tikhonov regularization of the problem. Second, we introduce an original regularized reconstruction method in which the regularization matrix is determined by space-uniformization of the variance of the reconstructed conductivities. Both methods are nonsupervised, i.e., all tuning parameters are automatically determined from the measured data. Tests performed on simulated and real data indicate that Tikhonov regularization provides results similar to those obtained with iterative methods, but with a much smaller amount of computations. Regularization using a variance uniformization constraint yields further improvements, particularly in the central region of the unknown object where attenuation is most severe. We anticipate that the variance uniformization approach could be adapted to iterative methods that preserve the nonlinearity of the forward problem. More generally, it appears as a useful tool for solving other severely ill-posed reconstruction problems such as eddy current tomography     

A computational investigation of microwave breast imaging using deformable reflector.

In recent years, active microwave breast imaging is increasingly being viewed as a promising complementary imaging modality for cancer detection. In this paper, we present a novel deformable reflector microwave tomography technique for noninvasive characterization of the breast tissue. In contrast to conventional multitransceiver designs, the proposed technique utilizes a continuously deformable reflector with metallic coating to acquire field measurements for imaging. Computational feasibility of the proposed technique to image heterogeneous dielectric tissue property is evaluated using simplified 2-D breast models. The robustness of the deformable reflector-based tomography technique in imaging the spatial distribution of the tissue dielectric property in the presence of measurement noise is investigated using first-order Tikhonov regularization. Preliminary results obtained for the 2-D breast models appear promising and indicate further investigation of the new microwave tomography technique for breast imaging.     

Solving the inverse problem of electrocardiography using a Duncan and Horn formulation of the Kalman filter

Numeric regularization methods most often used to solve the ill-posed inverse problem of electrocardiography are spatial and ignore the temporal nature of the problem. In this paper, a Kalman filter reformulation incorporated temporal information to regularize the inverse problem, and was applied to reconstruct left ventricular endocardial electrograms based on cavitary electrograms measured by a noncontact, multielectrode probe. These results were validated against in situ electrograms measured with an integrated, multielectrode basket-catheter. A three-dimensional, probe-endocardium model was determined from multiplane fluoroscopic images. The boundary element method was applied to solve the boundary value problem and determine a linear relationship between endocardial and probe potentials. The Duncan and Horn formulation of the Kalman filter was employed and was compared to the commonly used zero- and first-order Tikhonov spatial regularization as well as the Twomey temporal regularization method. Endocardial electrograms were reconstructed during both sinus and paced rhythms. The Paige and Saunders solution of the Duncan and Horn formulation reconstructed endocardial electrograms at an amplitude relative error of 13% (potential amplitude) which was superior to solutions obtained with zero-order Tikhonov (relative error, 31%), first-order Tikhonov (relative error, 19%), and Twomey regularization (relative error, 44%). Likewise, activation time error in the inverse solution using the Duncan and Horn formulation (2.9 ms) was smaller than that of zero-order Tikhonov (4.8 ms), first-order Tikhonov (5.4 ms), and Twomey regularization (5.8 ms). Therefore, temporal regularization based on the Duncan and Horn formulation of the Kalman filter improves the solution of the inverse problem of electrocardiography.     

A new spatiotemporal regularization approach for reconstruction of cardiac transmembrane potential patterns

The single-beat reconstruction of electrical cardiac sources from body-surface electrocardiogram data might become an important issue for clinical application. The feasibility and field of application of noninvasive imaging methods strongly depend on development of stable algorithms for solving the underlying ill-posed inverse problems. We propose a novel spatiotemporal regularization approach for the reconstruction of surface transmembrane potential (TMP) patterns. Regularization is achieved by imposing linearly formulated constraints on the solution in the spatial as well as in the temporal domain. In the spatial domain an operator similar to the surface Laplacian, weighted by a regularization parameter, is used. In the temporal domain monotonic nondecreasing behavior of the potential is presumed. This is formulated as side condition without the need of any regularization parameter. Compared to presuming template functions, the weaker temporal constraint widens the field of application because it enables the reconstruction of TMP patterns with ischemic and infarcted regions. Following the line of Tikhonov regularization, but considering all time points simultaneously, we obtain a linearly constrained sparse large-scale convex optimization problem solved by a fast interior point optimizer. We demonstrate the performance with simulations by comparing reconstructed TMP patterns with the underlying reference patterns.