Generalized optimal spatial filtering using a kernel approach with application to EEG classification

Common spatial patterns (CSP) has been widely used for finding the linear spatial filters which are able to extract the discriminative brain activities between two different mental tasks. However, the CSP is difficult to capture the nonlinearly clustered structure from the non-stationary EEG signals. To relax the presumption of strictly linear patterns in the CSP, in this paper, a generalized CSP (GCSP) based on generalized singular value decomposition (GSVD) and kernel method is proposed. Our method is able to find the nonlinear spatial filters which are formulated in the feature space defined by a nonlinear mapping through kernel functions. Furthermore, in order to overcome the overfitting problem, the regularized GCSP is developed by adding the regularized parameters. The experimental results demonstrate that our method is an effective nonlinear spatial filtering method.     

A Neural Network-Based Optimal Spatial Filter Design Method for Motor Imagery Classification

In this study, a novel spatial filter design method is introduced. Spatial filtering is an important processing step for feature extraction in motor imagery-based brain-computer interfaces. This paper introduces a new motor imagery signal classification method combined with spatial filter optimization. We simultaneously train the spatial filter and the classifier using a neural network approach. The proposed spatial filter network (SFN) is composed of two layers: a spatial filtering layer and a classifier layer. These two layers are linked to each other with non-linear mapping functions. The proposed method addresses two shortcomings of the common spatial patterns (CSP) algorithm. First, CSP aims to maximize the between-classes variance while ignoring the minimization of within-classes variances. Consequently, the features obtained using the CSP method may have large within-classes variances. Second, the maximizing optimization function of CSP increases the classification accuracy indirectly because an independent classifier is used after the CSP method. With SFN, we aimed to maximize the between-classes variance while minimizing within-classes variances and simultaneously optimizing the spatial filter and the classifier. To classify motor imagery EEG signals, we modified the well-known feed-forward structure and derived forward and backward equations that correspond to the proposed structure. We tested our algorithm on simple toy data. Then, we compared the SFN with conventional CSP and its multi-class version, called one-versus-rest CSP, on two data sets from BCI competition III. The evaluation results demonstrate that SFN is a good alternative for classifying motor imagery EEG signals with increased classification accuracy.     

Online Classification of Multiple Motor Imagery Tasks Using Filter Bank Based Maximum-a-Posteriori Common Spatial Pattern Filters

ObjectiveThe main objective of this paper is to propose a novel technique, called filter bank maximum a-posteriori common spatial pattern (FB-MAP-CSP) algorithm, for online classification of multiple motor imagery activities using electroencephalography (EEG) signals. The proposed technique addresses the overfitting issue of CSP in addition to utilizing the spectral information of EEG signals inside the framework of filter banks while extending it to more than two conditions.Materials and methodsThe classification of motor imagery signals is based upon the detection of event-related de-synchronization (ERD) phenomena in the μ and β rhythms of EEG signals. Accordingly, two modifications in the existing MAP-CSP technique are presented: (i) The (pre-processed) EEG signals are spectrally filtered by a bank of filters lying in the μ and β brainwave frequency range, (ii) the framework of MAP-CSP is extended to deal with multiple (more than two) motor imagery tasks classification and the spatial filters thus obtained are calculated for each sub-band, separately. Subsequently, the most imperative features over all sub-bands are selected and un-regularized linear discriminant analysis is employed for classification of multiple motor imagery tasks.ResultsPublicly available dataset (BCI Competition IV Dataset I) is used to validate the proposed method i.e. FB-MAP-CSP. The results show that the proposed method yields superior classification results, in addition to be computationally more efficient in the case of online implementation, as compared to the conventional CSP based techniques and its variants for multiclass motor imagery classification.ConclusionThe proposed FB-MAP-CSP algorithm is found to be a potential / superior method for classifying multi-condition motor imagery EEG signals in comparison to FBCSP based techniques.     

Motor Imagery EEG Spectral-Spatial Feature Optimization Using Dual-Tree Complex Wavelet and Neighbourhood Component Analysis

BackgroundFrequency band optimization improves the performance of common spatial pattern (CSP) in motor imagery (MI) tasks classification because MI-related electroencephalograms (EEGs) are highly frequency specific. Many variants of CSP algorithm divided the EEG into various sub bands and then applied CSP. However, the feature dimension of MI-EEG data increases with addition of frequency sub bands and requires efficient feature selection algorithms. The performance of CSP also depends on filtering techniques.MethodIn this study, we designed a dual tree complex wavelet transform based filter bank to filter the EEG into sub bands, instead of traditional filtering methods, which improved the spatial feature extraction efficiency. Further, after filtering EEG into different sub bands, we extracted spatial features from each sub band using CSP and optimized them by a proposed supervised learning framework based on neighbourhood component analysis (NCA). Subsequently, a support vector machine (SVM) is trained to perform classification.ResultsAn experimental study, conducted on two datasets (BCI Competition IV (Dataset 2b), and BCI competition III (Dataset IIIa)), validated the MI classification effectiveness of the proposed method in comparison with standard algorithms such as CSP, Filter bank CSP (CSP), and Discriminative FBCSP (DFBCSP). The average classification accuracy obtained by the proposed method for BCI Competition IV (Dataset 2b), and BCI Competition III (Dataset IIIa) are 84.02 ± 12.2 and 89.1 ± 7.50, respectively and found significant than that achieved by standard methods.ConclusionAchieved superior results suggest that the proposed algorithm can improve the performance of MI-based Brain-computer interface devices.     

Regularized common spatial patterns with subject-to-subject transfer of EEG signals

In the context of brain-computer interface (BCI) system, the common spatial patterns (CSP) method has been used to extract discriminative spatial filters for the classification of electroencephalogram (EEG) signals. However, the classification performance of CSP typically deteriorates when a few training samples are collected from a new BCI user. In this paper, we propose an approach that maintains or improves the recognition accuracy of the system with only a small size of training data set. The proposed approach is formulated by regularizing the classical CSP technique with the strategy of transfer learning. Specifically, we incorporate into the CSP analysis inter-subject information involving the same task, by minimizing the difference between the inter-subject features. Experimental results on two data sets from BCI competitions show that the proposed approach greatly improves the classification performance over that of the conventional CSP method; the transformed variant proved to be successful in almost every case, based on a small number of available training samples.     

Modelling geographical patterns in species richness using eigenvector-based spatial filters

Aim To test the mechanisms driving bird species richness at broad spatial scales using eigenvector‐based spatial filtering. Location South America. Methods An eigenvector‐based spatial filtering was applied to evaluate spatial patterns in South American bird species richness, taking into account spatial autocorrelation in the data. The method consists of using the geographical coordinates of a region, based on eigenanalyses of geographical distances, to establish a set of spatial filters (eigenvectors) expressing the spatial structure of the region at different spatial scales. These filters can then be used as predictors in multiple and partial regression analyses, taking into account spatial autocorrelation. Autocorrelation in filters and in the regression residuals can be used as stopping rules to define which filters will be used in the analyses. Results Environmental component alone explained 8% of variation in richness, whereas 77% of the variation could be attributed to an interaction between environment and geography expressed by the filters (which include mainly broad‐scale climatic factors). Regression coefficients of environmental component were highest for AET. These results were unbiased by short‐scale spatial autocorrelation. Also, there was a significant interaction between topographic heterogeneity and minimum temperature. Conclusion Eigenvector‐based spatial filtering is a simple and suitable statistical protocol that can be used to analyse patterns in species richness taking into account spatial autocorrelation at different spatial scales. The results for South American birds are consistent with the climatic hypothesis, in general, and energy hypothesis, in particular. Habitat heterogeneity also has a significant effect on variation in species richness in warm tropical regions.     

Sparse spatial filter via a novel objective function minimization with smooth ℓ1 regularization

Common spatial pattern (CSP) method is widely used in brain machine interface (BMI) applications to extract features from the multichannel neural activity through a set of spatial projections. These spatial projections minimize the Rayleigh quotient (RQ) as the objective function, which is the variance ratio of the classes. The CSP method easily overfits the data when the number of training trials is not sufficiently large and it is sensitive to daily variation of multichannel electrode placement, which limits its applicability for everyday use in BMI systems. To overcome these problems, the amount of channels that is used in projections, should be limited to some adequate number. We introduce a spatially sparse projection (SSP) method that exploits the unconstrained minimization of a new objective function with approximated ?₁ penalty. Unlike the RQ, this new objective function depends on the magnitude of the sparse filter. The SSP method is employed to classify the multiclass ECoG and two class EEG data sets. We compared our results with a recently introduced sparse CSP solution based on ?₀ norm. Our method outperforms the standard CSP method and provides comparable results to ?₀ norm based solution and it is associated with less computational complexity. We also conducted several simulation studies on the effect of noisy channel and intersession variability on the performance of the CSP and sparse filters.     

Robust filtering circuit design for stochastic gene networks under intrinsic and extrinsic molecular noises

How to design a robust gene network to tolerate more intrinsic kinetic parameter variations and to attenuate more extrinsic environmental noises to achieve a desired filtering level will be an important topic for systems biology and synthetic biology. At present, there is no good systematic design method to achieve robust gene network design. In this study, a gene network suffering from intrinsic kinetic parameter fluctuations and extrinsic environmental noises is modeled as a Langevin equation with state-dependent stochastic noises. Based on the nonlinear stochastic filtering theory, a systematic gene circuit design method is proposed to make gene networks improve their robustness to tolerate more intrinsic noises and to attenuate extrinsic noises to a prescribed filtering level. The robust gene network design principles have not only yielded a comprehensive design theory of robust gene networks, but also gained valuable insights into the molecular noise filtering of gene networks from the systematic perspective.     

The importance of spatial scale for trait–abundance relations

The concept of community assembly through trait‐based environmental filtering has played a key role in our understanding of how communities change over space and time, however, the importance of spatial scale in the filtering process remains unclear. We propose that different environmental filters may operate at different spatial scales, and that filters at finer scales would be nested within those acting at coarser scales. We tested for the existence of spatially nested sets of trait‐based filters in a temperate native grassland by applying the recently proposed maximum entropy (MaxEnt) approach to trait‐based community assembly, which we extend through a trait selection procedure. We found that different traits were important in influencing the abundances of species at the three different spatial scales examined (micro‐habitat, habitat, landscape), supporting the idea that trait based filtering processes operating at coarse spatial scales can be quite distinct from those operating at fine scales. Despite this result, we identified several traits which were frequently related to abundance at all spatial scales. Taken together, our results support the proposition that trait‐based environmental filters at finer spatial scales are nested within those operating at coarser scales. We compared our results to those obtained using a simpler trait‐by‐trait analytical approach (correlation analysis and MaxEnt on individual traits). The capacity for MaxEnt to incorporate multiple traits simultaneously provided unique insights into the important traits at each spatial scale and presents significant advantages over existing univariate and multivariate approaches.     

一种滤除医学影像噪声的混合滤波算法

目的：医学影像在获取、存储、传输过程中会不同程度地受到噪声污染,这极大影像了其在临床诊疗中的应用。为了有效地滤除医学影像噪声,提出了一种混合滤波算法。方法：该算法首先将含有高斯和椒盐噪声的图像进行形态学开运算,然后对开运算后的图像进行二维小波分解,得到高频和低频小波分解系数。保留低频系数不变,将高频系数经过维纳滤波器进行滤波,最后进行小波系数重构。结果：采用该混合滤波算法、小波阚值去噪、中值滤波、维纳滤波分别对含有混合噪声的医学影像分别进行滤除噪声处理,该滤波算法去噪后影像的PSNR值明显高于其他三种方法。结论：该混合滤波算法是一种较为有效的医学影像噪声滤除方法。     

A Compact Nanoplasmonics Filter and Intersection Structure Based on Utilizing a Slot Cavity and a Fabry–Perot Resonator

By combining a Fabry–Perot (FP) cavity with a slot cavity, a compact filter structure is proposed. The peak resonance wavelength is determined by applying the FP resonance condition of the FP cavity. The relationship between filtering wavelength and cavity parameters is investigated. The results show that the filtering wavelength can be manipulated by changing the nanocavities' parameters. By using the finite difference time domain method, the theoretical predictions are confirmed. An intersection structure for nanoplasmonic waveguides is proposed and designed by utilizing two perpendicular filters. In addition to having compact dimensions, the proposed arrangement provides higher throughput and low cross talk. The proposed structure can be useful for designing compact integrated nanoplasmonic circuits.     

On the Pharyngeal Feeding Filter of the Salp Pegea confoederata (Tunicata: Thaliacea)

In Pegea, scanning electron microscopy of what appear to be the least damaged portions of the filter shows that it has a regular rectangular mesh consisting of thick (100 nm) fibres at right angles to thinner (50 nm) fibres. The rectangular pores of the filter are around 3.3 × 0.57 μm. These measured values from filters that have suffered shrinkage (to an uncertain degree) during preparation are considered to indicate that the actual pore size in life is some 4.0 × 0.7 μm. The mucous-net feeding filter of salps differs from that of other tunicates since flow through it results from muscular activity. Calculations based on the estimated pore size and filtering rate suggest that during part of the filtering cycle, the pressure drop across the filter is considerably greater than that across other tunicate mucous-net filters.     

A model of human pattern perception: association fields for adaptive spatial filters.

Visual neurons in the primary visual cortex 'look' at the retinal image through a four-dimensional array of spatial receptive fields (filter-elements): two spatial dimensions and, at each spatial location, two Fourier dimensions of spatial frequency and orientation. In general, visual objects activate filter-elements along each of these dimensions, suggesting a need for some kind of linking mechanism that determines whether two or more filter-elements are responding to the same or different contours or objects. In the spatial domain, a (spatial) association field between filter-elements, arranged to form first-order curves, has been inferred as a flexible method by which different parts of extended (luminance) contours become associated (Field et al., 1993). Linking has also been explored between filters selective for different regions in Fourier space (e.g. Georgeson and Meese, 1997). Perceived structure of stationary plaids suggests that spatial filtering is adaptive: synthetic filters can be created by the linear summation of basis-filters across orientation or spatial frequency in a stimulus-dependent way. For example, a plaid with a pair of sine-wave components at +/-45 deg looks like a blurred checkerboard; a structure that can be understood if features are derived after linear summation of spatial filters at different orientations. However, the addition of an oblique third-harmonic component causes the plaid to perceptually segment into overlapping oblique contours. This result can be understood if filters are summed across spatial frequency, but, in this case, treated independently across orientation. In the present paper, the architecture of an association field is proposed to permit linking and segmentation of filter-elements across spatial frequency and orientation. Three types of link are proposed: (1) A chain of constructive links around sites of common spatial frequency but different orientation, to promote binding of filters across orientation; (2) Constructive links between sites with common orientation but different spatial frequency, to promote binding of filters across spatial frequency; (3) Long-range links between sites of common spatial frequency but different orientation, whose activation and role are determined by activity in a higher spatial frequency band. A model employing the proposed network of links is consistent with at least six previously reported effects on the perception of briefly presented stationary plaids.     

Empirical mode decomposition based filtering techniques for power line interference reduction in electrocardiogram using various adaptive structures and subtraction methods

Electrocardiogram (ECG) is a vital sign monitoring measurement of the cardiac activity. One of the main problems in biomedical signals like electrocardiogram is the separation of the desired signal from noises caused by power line interference, muscle artifacts, baseline wandering and electrode artifacts. Different types of digital filters are used to separate signal components from unwanted frequency ranges. Adaptive filter is one of the primary methods to filter, because it does not need the signal statistic characteristics. In contrast with Fourier analysis and wavelet methods, a new technique called EMD, a fully data-driven technique is used. It is an adaptive method well suited to analyze biomedical signals. This paper foregrounds an empirical mode decomposition based two-weight adaptive filter structure to eliminate the power line interference in ECG signals. This paper proposes four possible methods and each have less computational complexity compared to other methods. These methods of filtering are fully a signal-dependent approach with adaptive nature, and hence it is best suited for denoising applications. Compared to other proposed methods, EMD based direct subtraction method gives better SNR irrespective of the level of noises.     

Generalized gradient schemes for the measurement of two-dimensional image motion

This paper describes a procedure for recovering the global velocity of an image by incorporating spatial filtering, and, optionally, temporal filtering, into a scheme that employs a generalized version of the gradient algorithm of motion detection. Motion within a patch is analysed by six parallel channels, each incorporating a different spatiotemporal filter. Advantageous features of this scheme are: (a) global velocity is derived directly, without first computing local velocity at a number of image locations; (b) the filters compute first derivatives rather than second derivatives, making the scheme potentially more resistant to noise than certain other schemes; (c) two of the six filters can be chosen almost completely arbitrarily, and can therefore be tailored to maximize signal reliability, and (d) the measurement of velocity can be made as local or as global as desired by altering the size of the patch that is viewed by the filters. An analogous scheme is derived for the measurement of rotation, as well as expansion or contraction of the image.     

Examining the effects of one- and three-dimensional spatial filtering analyses in magnetoencephalography

Spatial filtering, or beamforming, is a commonly used data-driven analysis technique in the field of Magnetoencephalography (MEG). Although routinely referred to as a single technique, beamforming in fact encompasses several different methods, both with regard to defining the spatial filters used to reconstruct source-space time series and in terms of the analysis of these time series. This paper evaluates two alternative methods of spatial filter construction and application. It demonstrates how encoding different requirements into the design of these filters has an effect on the results obtained. The analyses presented demonstrate the potential value of implementations which examine the timeseries projections in multiple orientations at a single location by showing that beamforming can reconstruct predominantly radial sources in the case of a multiple-spheres forward model. The accuracy of source reconstruction appears to be more related to depth than source orientation. Furthermore, it is shown that using three 1-dimensional spatial filters can result in inaccurate source-space time series reconstruction. The paper concludes with brief recommendations regarding reporting beamforming methodologies in order to help remove ambiguity about the specifics of the techniques which have been used.     

Air-sampled Filter Analysis for Endotoxins and DNA Content

Outdoor aerosol research commonly uses particulate matter sampled on filters. This procedure enables various characterizations of the collected particles to be performed in parallel. The purpose of the method presented here is to obtain a highly accurate and reliable analysis of the endotoxin and DNA content of bio-aerosols extracted from filters. The extraction of high molecular weight organic molecules, such as lipopolysaccharides, from sampled filters involves shaking the sample in a pyrogen-free water-based medium. The subsequent analysis is based on an enzymatic reaction that can be detected using a turbidimetric measurement. As a result of the high organic content on the sampled filters, the extraction of DNA from the samples is performed using a commercial DNA extraction kit that was originally designed for soils and modified to improve the DNA yield. The detection and quantification of specific microbial species using quantitative polymerase chain reaction (q-PCR) analysis are described and compared with other available methods.     

Processing visual signals with nonlinear spatial filters

Summary The properties of nonlinear spatial filters as a major part of the peripheral nervous system are investigated with respect to processing of two types of signals: a deterministic stepfunction and Gaussian noise. The nonlinearity of the nerve cell is treated as a threshold element. It is shown that certain unfavorable characteristics of linear filters do not occur in such nonlinear filters. The basic nonlinear effects of combined space-time-filtering are demonstrated by using bandpass filters.Time- and space-dependent noise is applied to the nonlinear bandpass. The two subsystems formed by the linear bandpass section and the threshold are treated separately.Two examples for the application of nonlinear spatial filtering are given.This paper contains results of a thesis submitted to the Fachbereich Biologie der Johannes Gutenberg-Universität, Mainz, in partial fulfillment of the requirements for the degree of a Dr. rer. nat.The author is grateful to Prof. Dr.-Ing. W. v. Seelen for his continual guidance and support.     

Using eigenstructure decompositions of time-varying autoregressions in common spatial patterns-based EEG signal classification

Brain–computer interfaces based on common spatial patterns (CSP) depend on the operational frequency bands of the events to be discriminated. This problem has been addressed through sub-band decompositions of the electroencephalographic signals using filter banks, then the performance relies on the number of filters that are stacked and the criteria to select their bandwidths. Here, we propose an alternative approach based on an eigenstructure decomposition of the signals’ time-varying autoregressions (TVAR). The eigen-based decomposition of the TVAR allows for subject-specific estimation of the principal time-varying frequencies, then such principal eigencomponents can be used in the traditional CSP-based classification. We show through a series of numerical experiments that the proposed classification scheme can achieve a performance which is comparable with the one obtained through the filter bank-based approach. However, our method does not rely on a preliminary selection of a frequency band, yet good performance is achieved under realistic conditions (such as reduced number of sensors and small amount of training data) independently of the time interval selected.     

Low-pass filtering, a new method of fractal analysis: application to PET images of pulmonary blood flow.

The pattern of a spatial structure that repeats itself independently of the scale of magnification or resolution is often characterized by a fractal dimension (D). Two-dimensional low-pass filtering, which may serve as a method to assess D, was applied to functional images of pulmonary perfusion measured by positron emission tomography. The corner frequency of a low-pass filter is inversely proportional to the resolution scale. The method was applied to three types of images: random noise images, synthetic fractal images, and positron emission tomographic images of pulmonary perfusion. Images were processed with two-dimensional low-pass filters of decreasing corner frequencies, and a spatial heterogeneity index, the coefficient of variation, was calculated for each low-pass-filtered image. The natural logarithm of the coefficient of variation scaled linearly with the natural logarithm of the resolution scale for the PET images studied (average R(2) = 0.99). D ranged from 1.25 to 1.36 for the residual distribution of pulmonary perfusion after vertical gradients were removed by linear regression. D of the same data without removal of vertical gradients ranged from 1.11 to 1.14, but the fractal plots had systematic deviations from linearity and a lower linear correlation coefficient (R(2) = 0. 96). The method includes all data in the lung field and is insensitive to the effects of misregistration. We conclude that low-pass filtering offers new insights into the interpretation of D of two-dimensional functional images as a measure of the frequency content of spatial heterogeneity.