Recursively Applied And Projected Multiple Signal Classification Research Articles

Subspace based Multiple Constrained Minimum Variance (SMCMV) beamformers

In Magnetoencephalography (MEG) and Electroencephalography (EEG) two popular approaches are often used for spatial localization of focal task- or stimuli-related brain activations. One is Multiple Signal Classification (MUSIC) approach in the form of Recursively Applied and Projected (RAP) or Truncated RAP (TRAP) MUSIC algorithms. Another one is Multiple Constrained Minimum Variance (MCMV) beamformer method capable of dealing with multiple correlated activations. Considering simplicity, accuracy and computational efficiency both have their advantages and disadvantages. Using these two techniques as a starting point, three main developments were made in this study. First, we introduced novel Subspace based MCMV (or SMCMV) beamformers whose localizer functions combine MUSIC and MCMV localizers. Second, we showed analytically that SMCMV localizers in principle allow precise identification of n arbitrarily correlated sources irrespective to their strength in exactly n scans of the brain volume. Third, using extensive simulations and ANOVA statistical analyses we showed that on average SMCMV outperforms both the TRAP MUSIC and MCMV Multi-step Iterative Approach (MIA) procedure, currently the most accurate MCMV algorithm to our knowledge, with respect to localization accuracy and the number of successfully identified sources. Importantly, this was demonstrated for situations when the noise covariance could not be estimated precisely, signal to noise ratios were small, source correlations were significant and larger numbers of sources were involved. SMCMV advantage held for both MEG and EEG modalities. In addition we illustrated the SMCMV method by applying it to a real MEG Auditory Steady State Response (ASSR) experiment.

3D heart sound source localization via combinational subspace methods for long-term heart monitoring

Abstract Heart sound is a key mean for heart monitoring and a common known early diagnosis modality. In this paper, by employing a multiple channel sound recording system and implementing a spatiotemporal information extraction process, a powerful approach is proposed for heart monitoring. Use of the extracted spatiotemporal information of the heart sound, which in turn could lead to detection of the time duration and the heart abnormalities source locations, gives a clinical contribution to the diagnosis of heart valvular diseases. Since the heart valves have very small distances from each other and are located in a reverberant environment of chest and its surrounding muscles, we take the advantages of the group-delay information of the Recursively Applied and Projected-MUltiple SIgnal Classification (RAP-MUSIC) method to localize the active heart valves in the S1, systole, S2, and diastole phases of the heart sound. The proposed algorithm is applied to a simulated database and compared with the MUltiple SIgnal Classification (MUSIC), RAPMUSIC and group delayed MUSIC algorithms. The comparison shows the proposed combinational method has the highest resolution in the simulated environment and more accuracy when sources are very close. In the following, the proposed algorithm is applied to some normal and abnormal heart sounds recorded by the employed microphone array. The obtained results indicate that the proposed method can localize the heart valves in real conditions. Moreover, it is shown that via this approach, the extra abnormal sound sources in the heart of the patients, if exist, could be properly detected and localized. This 3D heart valve localization method is an appropriate approach suitable to be employed in long-term heart monitoring instruments.

Self-Consistent MUSIC: An approach to the localization of true brain interactions from EEG/MEG data

MUltiple SIgnal Classification (MUSIC) is a standard localization method which is based on the idea of dividing the vector space of the data into two subspaces: signal subspace and noise subspace. The brain, divided into several grid points, is scanned entirely and the grid point with the maximum consistency with the signal subspace is considered as the source location. In one of the MUSIC variants called Recursively Applied and Projected MUSIC (RAP-MUSIC), multiple iterations are proposed in order to decrease the location estimation uncertainties introduced by subspace estimation errors. In this paper, we suggest a new method called Self-Consistent MUSIC (SC-MUSIC) which extends RAP-MUSIC to a self-consistent algorithm. This method, SC-MUSIC, is based on the idea that the presence of several sources has a bias on the localization of each source. This bias can be reduced by projecting out all other sources mutually rather than iteratively. While the new method is applicable in all situations when MUSIC is applicable we will study here the localization of interacting sources using the imaginary part of the cross-spectrum due to the robustness of this measure to the artifacts of volume conduction. For an odd number of sources this matrix is rank deficient similar to covariance matrices of fully correlated sources. In such cases MUSIC and RAP-MUSIC fail completely while the new method accurately localizes all sources. We present results of the method using simulations of odd and even number of interacting sources in the presence of different noise levels. We compare the method with three other source localization methods: RAP-MUSIC, dipole fit and MOCA (combined with minimum norm estimate) through simulations. SC-MUSIC shows substantial improvement in the localization accuracy compared to these methods. We also show results for real MEG data of a single subject in the resting state. Four sources are localized in the sensorimotor area at f=11Hz which is the expected region for the idle rhythm.

The localization of focal heart activity via body surface potential measurements: tests in a heterogeneous torso phantom

The non-invasive localization of focal heart activity via body surface potential measurements (BSPM) could greatly benefit the understanding and treatment of arrhythmic heart diseases. However, the in vivo validation of source localization algorithms is rather difficult with currently available measurement techniques. In this study, we used a physical torso phantom composed of different conductive compartments and seven dipoles, which were placed in the anatomical position of the human heart in order to assess the performance of the Recursively Applied and Projected Multiple Signal Classification (RAP-MUSIC) algorithm. Electric potentials were measured on the torso surface for single dipoles with and without further uncorrelated or correlated dipole activity. The localization error averaged 11 ± 5 mm over 22 dipoles, which shows the ability of RAP-MUSIC to distinguish an uncorrelated dipole from surrounding sources activity. For the first time, real computational modelling errors could be included within the validation procedure due to the physically modelled heterogeneities. In conclusion, the introduced heterogeneous torso phantom can be used to validate state-of-the-art algorithms under nearly realistic measurement conditions.

A hybrid algorithm for solving the EEG inverse problem from spatio-temporal EEG data

Epilepsy is a neurological disorder caused by intense electrical activity in the brain. The electrical activity, which can be modelled through the superposition of several electrical dipoles, can be determined in a non-invasive way by analysing the electro-encephalogram. This source localization requires the solution of an inverse problem. Locally convergent optimization algorithms may be trapped in local solutions and when using global optimization techniques, the computational effort can become expensive. Fast recovery of the electrical sources becomes difficult that way. Therefore, there is a need to solve the inverse problem in an accurate and fast way. This paper performs the localization of multiple dipoles using a global-local hybrid algorithm. Global convergence is guaranteed by using space mapping techniques and independent component analysis in a computationally efficient way. The accuracy is locally obtained by using the Recursively Applied and Projected-MUltiple Signal Classification (RAP-MUSIC) algorithm. When using this hybrid algorithm, a four times faster solution is obtained.

Evidence of a posterior cingulate involvement (Brodmann area 31) in dyslexia: A study based on source localization algorithm of event-related potentials

The study investigates the differences regarding the position of intracranial generators of P50 component of ERPs in 38 dyslexic children aged 11.47 ± 2.12 years compared with their 19 healthy siblings aged 12.21 ± 2.25. The dipoles were extracted by solving the inverse electromagnetic problem according to the recursively applied and projected multiple signal classification (RAP-MUSIC) algorithm approach. For improved localization of the main dipole the solutions were optimized using genetic algorithms. The statistical analysis revealed differences regarding the position of intracranial generators of low frequency of P50. Particularly, dyslexics showed main activity being located at posterior cingulate cortex (Brodmann's area 31) while controls exhibited main activity being located at retrosplenial cortex (Brodmann's area 30). These results may indicate a role for the posterior cingulate cortex in the pre-attentive processing operation of dyslexia beyond of its traditional function in terms of spatial attention and motor intention.

Source estimation of spikes by a combination of independent component analysis and RAP-MUSIC

We designed a combination of independent component analysis (ICA) and recursively applied and projected multiple signal classification (RAP-MUSIC) as a new approach to dipole source estimation of epileptiform discharges. The estimation is minimally influenced by subjective decisions in this analysis. A simulation study was performed by generating 10 EEG data matrices by means of a computer: each matrix included real background activity from a normal subject to which an array of simulated unaveraged spikes was added. Each discharge was a summation of two transients originating from slightly different “original dipole sources”. The simulated spikes in the unaveraged EEG data were extracted from the background by ICA as spatiotemporal components, each component having fixed potential field distribution and maximally independent waveform. The complete separation between spikes and background was objectively proven by reconstruction of the EEG from the decomposed components. RAP-MUSIC was performed based on the spatial information included in the epileptic ICA components. RAP-MUSIC does not involve subjective decisions such as selection of multiple local score peaks, determination of the number of dipoles or initial guesses of dipole parameters. In every simulated EEG data matrix, two dipoles close to the original sources were estimated. Their activities were also similar to those of the original sources. For comparison, the same simulated EEG data were averaged and subjected to RAP-MUSIC using eigen-decomposition of the covariance matrices. Only one dipole was estimated in every simulation by this conventional method and therefore the result of the present method was better. RAP-MUSIC based on ICA, thus, proved promising for source estimation of unaveraged epileptiform discharges.

Systematic source estimation of spikes by a combination of independent component analysis and RAP-MUSIC: II: Preliminary clinical application

Objectives: We tried to estimate epileptic sources by a combination of independent component analysis (ICA) and recursively applied and projected multiple signal classification (RAP-MUSIC) in real epileptiform EEG discharges.Methods: EEG data including an array of spikes from 3 patients were decomposed by ICA, and source estimation was performed by applying RAP-MUSIC to the spatial information defined by the set of ICA components that showed epileptiform activity in their waveform. Sources were also estimated from the same data using RAP-MUSIC based on eigen-decomposition of the covariance matrix of averaged spikes, and common spatial pattern decomposition for comparison.Results: RAP-MUSIC based on ICA could estimate generally correct epileptic sources in the 3 patients, and its results were better than those of the other methods, when compared to intracerebral data. The present analysis proceeded without introduction of subjective decision after data selection. The separation of epileptiform discharges from the background is essential for this analysis, and was successfully performed in the real EEG data.Conclusions: RAP-MUSIC based on ICA appears promising for estimation of epileptic sources with minimal dependence on subjective decisions in the process of analysis. In particular, it was not necessary to select the number of sources.

Systematic source estimation of spikes by a combination of independent component analysis and RAP-MUSIC: I: Principles and simulation study

Objectives: We propose a combination of independent component analysis (ICA) and recursively applied and projected multiple signal classification (RAP-MUSIC) as a new approach to dipole source estimation of epileptiform discharges. The method is minimally dependent on subjective decisions.Methods: Ten electroencephalographic (EEG) data matrices were generated by computer, each matrix including real background activity from a normal subject and an array of added simulated spikes. Each spike was a summation of two transients originating from slightly different ‘original dipole sources’. The unaveraged EEG matrices were decomposed by ICA, and source estimation was performed by applying RAP-MUSIC to the spatial information defined by the ICA components showing epileptiform activity in their waveform. For comparison, dipoles were also estimated from the same matrices using two existing methods: RAP-MUSIC based on eigen-decomposition of the covariance matrices of averaged spikes and common spatial pattern decomposition.Results: In every simulated EEG data matrix, two dipoles close to the original sources were estimated by the present method. Their unaveraged activities were also similar to those of the original sources. The two existing methods gave less precise results than the proposed method.Conclusions: RAP-MUSIC based on ICA thus proved promising for source estimation of unaveraged epileptiform discharges.

Paired MEG data set source localization using recursively applied and projected (RAP) MUSIC.

An important class of experiments in functional brain mapping involves collecting pairs of data corresponding to separate "Task" and "Control" conditions. The data are then analyzed to determine what activity occurs during the Task experiment but not in the Control. Here we describe a new method for processing paired magnetoencephalographic (MEG) data sets using our recursively applied and projected multiple signal classification (RAP-MUSIC) algorithm. In this method the signal subspace of the Task data is projected against the orthogonal complement of the Control data signal subspace to obtain a subspace which describes spatial activity unique to the Task. A RAP-MUSIC localization search is then performed on this projected data to localize the sources which are active in the Task but not in the Control data. In addition to dipolar sources, effective blocking of more complex sources, e.g., multiple synchronously activated dipoles or synchronously activated distributed source activity, is possible since these topographies are well-described by the Control data signal subspace. Unlike previously published methods, the proposed method is shown to be effective in situations where the time series associated with Control and Task activity possess significant cross correlation. The method also allows for straightforward determination of the estimated time series of the localized target sources. A multiepoch MEG simulation and a phantom experiment are presented to demonstrate the ability of this method to successfully identify sources and their time series in the Task data.