Comparison of methods for detecting nondeterministic BOLD fluctuation in fMRI

Functional MR imaging (fMRI) has been used in detecting neuronal activation and intrinsic blood flow fluctuations in the brain cortex. This article is aimed for comparing the methods for analyzing the nondeterministic flow fluctuations. Fast Fourier Transformation (FFT), cross correlation (CC), spatial principal component analysis (sPCA), and independent component analysis (sICA) were compared. 15 subjects were imaged at 1.5 T. Three quantitative measures were compared: (1) The number of subjects with identifiable fluctuation, (2) the volume, and (3) mean correlation coefficient (MCC) of the detected voxels. The focusing on cortical structures and the overall usability were qualitatively assessed. sICA was spatially most accurate but time consuming, robust, and detected voxels with high temporal synchrony. The CC and FFT were fast suiting primary screening. The CC detected highest temporal synchrony but the subjective detection for reference vector produced excess variance of the detected volumes. The FFT and sPCA were not spatially accurate and did not detect adequate temporal synchrony of the voxels.     

A statistical fMRI model for differential T2* contrast incorporating T1 and T2* of gray matter

Relaxation parameter estimation and brain activation detection are two main areas of study in magnetic resonance imaging (MRI) and functional magnetic resonance imaging (fMRI). Relaxation parameters can be used to distinguish voxels containing different types of tissue whereas activation determines voxels that are associated with neuronal activity. In fMRI, the standard practice has been to discard the first scans to avoid magnetic saturation effects. However, these first images have important information on the MR relaxivities for the type of tissue contained in voxels, which could provide pathological tissue discrimination. It is also well-known that the voxels located in gray matter (GM) contain neurons that are to be active while the subject is performing a task. As such, GM MR relaxivities can be incorporated into a statistical model in order to better detect brain activation. Moreover, although the MR magnetization physically depends on tissue and imaging parameters in a nonlinear fashion, a linear model is what is conventionally used in fMRI activation studies. In this study, we develop a statistical fMRI model for Differential T₂^? ConTrast Incorporating T₁ and T₂^? of GM, so-called DeTeCT-ING Model, that considers the physical magnetization equation to model MR magnetization; uses complex-valued time courses to estimate T₁ and T₂^? for each voxel; then incorporates gray matter MR relaxivities into the statistical model in order to better detect brain activation, all from a single pulse sequence by utilizing the first scans.     

Reliability of the depth-dependent high-resolution BOLD hemodynamic response in human visual cortex and vicinity

Functional magnetic resonance imaging (fMRI) often relies on a hemodynamic response function (HRF), the stereotypical blood oxygen level dependent (BOLD) response elicited by a brief (< 4 s) stimulus. Early measurements of the HRF used coarse spatial resolutions (≥ 3 mm voxels) that would generally include contributions from white matter, gray matter, and the extra-pial compartment (the space between the pial surface and skull including pial blood vessels) within each voxel. To resolve these contributions, high-resolution fMRI (0.9-mm voxels) was performed at 3 T in early visual cortex and its apposed white-matter and extra-pial compartments. The results characterized the depth dependence of the HRF and its reliability during nine fMRI sessions. Significant HRFs were observed in white-matter and extra-pial compartments as well as in gray matter. White-matter HRFs were faster and weaker than in the gray matter, while extra-pial HRFs were comparatively slower and stronger. Depth trends of the HRF peak amplitude were stable throughout a broad depth range that included all three compartments for each session. Across sessions, however, the depth trend of HRF peak amplitudes was stable only in the white matter and deep-intermediate gray matter, while there were strong session-to-session variations in the superficial gray matter and the extra-pial compartment. Thus, high-resolution fMRI can resolve significant and dynamically distinct HRFs in gray matter, white matter, and extra-pial compartments.     

Strategies for reducing large fMRI data sets for independent component analysis

In independent component analysis (ICA), principal component analysis (PCA) is generally used to reduce the raw data to a few principal components (PCs) through eigenvector decomposition (EVD) on the data covariance matrix. Although this works for spatial ICA (sICA) on moderately sized fMRI data, it is intractable for temporal ICA (tICA), since typical fMRI data have a high spatial dimension, resulting in an unmanageable data covariance matrix. To solve this problem, two practical data reduction methods are presented in this paper. The first solution is to calculate the PCs of tICA from the PCs of sICA. This approach works well for moderately sized fMRI data; however, it is highly computationally intensive, even intractable, when the number of scans increases. The second solution proposed is to perform PCA decomposition via a cascade recursive least squared (CRLS) network, which provides a uniform data reduction solution for both sICA and tICA. Without the need to calculate the covariance matrix, CRLS extracts PCs directly from the raw data, and the PC extraction can be terminated after computing an arbitrary number of PCs without the need to estimate the whole set of PCs. Moreover, when the whole data set becomes too large to be loaded into the machine memory, CRLS-PCA can save data retrieval time by reading the data once, while the conventional PCA requires numerous data retrieval steps for both covariance matrix calculation and PC extractions. Real fMRI data were used to evaluate the PC extraction precision, computational expense, and memory usage of the presented methods.     

CORSICA: correction of structured noise in fMRI by automatic identification of ICA components

When applied to functional magnetic resonance imaging (fMRI) data, spatial independent component analysis (sICA), a data-driven technique that addresses the blind source separation problem, seems able to extract components specifically related to physiological noise and brain movements. These components should be removed from the data to achieve structured noise reduction and improve any subsequent detection and analysis of signal fluctuations related to neural activity. We propose a new automatic method called CORSICA (CORrection of Structured noise using spatial Independent Component Analysis) to identify the components related to physiological noise, using prior information on the spatial localization of the main physiological fluctuations in fMRI data. As opposed to existing spectral priors, which may be subject to aliasing effects for long-TR data sets (typically acquired with TR >1 s), such spatial priors can be applied to fMRI data, regardless of the TR of the acquisitions. By comparing the proposed automatic selection to a manual selection performed visually by a human operator, we first show that CORSICA is able to identify the noise-related components for long-TR data with a high sensitivity and a specificity of 1. On short-TR data sets, we validate that the proposed method of noise reduction allows a substantial improvement of the signal-to-noise ratio evaluated at the cardiac and respiratory frequencies, even in the gray matter, while preserving the main fluctuations related to neural activity.     

Performance of blind source separation algorithms for fMRI analysis using a group ICA method

Independent component analysis (ICA) is a popular blind source separation technique that has proven to be promising for the analysis of functional magnetic resonance imaging (fMRI) data. A number of ICA approaches have been used for fMRI data analysis, and even more ICA algorithms exist; however, the impact of using different algorithms on the results is largely unexplored. In this paper, we study the performance of four major classes of algorithms for spatial ICA, namely, information maximization, maximization of non-Gaussianity, joint diagonalization of cross-cumulant matrices and second-order correlation-based methods, when they are applied to fMRI data from subjects performing a visuo-motor task. We use a group ICA method to study variability among different ICA algorithms, and we propose several analysis techniques to evaluate their performance. We compare how different ICA algorithms estimate activations in expected neuronal areas. The results demonstrate that the ICA algorithms using higher-order statistical information prove to be quite consistent for fMRI data analysis. Infomax, FastICA and joint approximate diagonalization of eigenmatrices (JADE) all yield reliable results, with each having its strengths in specific areas. Eigenvalue decomposition (EVD), an algorithm using second-order statistics, does not perform reliably for fMRI data. Additionally, for iterative ICA algorithms, it is important to investigate the variability of estimates from different runs. We test the consistency of the iterative algorithms Infomax and FastICA by running the algorithm a number of times with different initializations, and we note that they yield consistent results over these multiple runs. Our results greatly improve our confidence in the consistency of ICA for fMRI data analysis.     

Quantification of venous blood signal contribution to BOLD functional activation in the auditory cortex at 3 T

Most modern techniques for functional magnetic resonance imaging (fMRI) rely on blood-oxygen-level-dependent (BOLD) contrast as the basic principle for detecting neuronal activation. However, the measured BOLD effect depends on a transfer function related to neurophysiological changes accompanying electrical neural activation. The spatial accuracy and extension of the region of interest are determined by vascular effect, which introduces incertitude on real neuronal activation maps. Our efforts have been directed towards the development of a new methodology that is capable of combining morphological, vascular and functional information; obtaining new insight regarding foci of activation; and distinguishing the nature of activation on a pixel-by-pixel basis. Six healthy volunteers were studied in a parametric auditory functional experiment at 3 T; activation maps were overlaid on a high-resolution brain venography obtained through a novel technique. The BOLD signal intensities of vascular and nonvascular activated voxels were analyzed and compared: it was shown that nonvascular active voxels have lower values for signal peak (P<10(-7)) and area (P<10(-8)) with respect to vascular voxels. The analysis showed how venous blood influenced the measured BOLD signals, supplying a technique to filter possible venous artifacts that potentially can lead to misinterpretation of fMRI results. This methodology, although validated in the auditory cortex activation, maintains a general applicability to any cortical fMRI study, as the basic concepts on which it relies on are not limited to this cortical region. The results obtained in this study can represent the basis for new methodologies and tools that are capable of adding further characterization to the BOLD signal properties.     

The effect of artifacts on dependence measurement in fMRI

The study of effective connectivity by means of neuroimaging depends on the measurement of similarity between activity patterns at different locations in the brain, without necessarily presupposing a particular model for this dependence. When these interactions are measured using functional magnetic resonance imaging (fMRI) techniques, however, imaging and physiological artifacts create patterns of dependence that may be unrelated to cortical activity. We demonstrate some of these effects through the measurement of short-range dependencies present in fMRI scans of the primary visual cortex (V1) in the anaesthetized macaque monkey. High-field (4.7 T) fMRI scans were conducted to measure responses based on the blood oxygen level-dependent contrast mechanism, during periods of no sensory stimulation and of visual stimulation with rotating polar-transformed checkerboard gratings. Dependence between the haemodynamic activity at different spatial locations (i.e., different voxels) was measured using correlation, mutual information and functional covariance. Particular attention was paid to understanding the sources of spurious dependence that may be observed during such investigations. Two main effects were detected: (a) short-range correlations introduced by the process of image reconstruction and (b) perturbations in the haemodynamic response caused by breathing. The image reconstruction artifacts were shown to create an artificially high short-range dependence in the readout direction of the scan, and the breathing artifacts caused enhanced short-range dependence in both the readout and phase-encode directions. Additional dependence in the phase-encode direction due to image-ghosting is also possible but will not be discussed in this report, as it can be alleviated by fine adjustment of preemphasis (elimination of eddy currents). A technique is described for removing breathing artifacts, and the effect of breathing on the apparent dependence between voxels is illustrated. The correlation of haemodynamic activity with the stimulus was found to be affected by breathing, although this effect can be neutralised by averaging the haemodynamic responses over many repetitions of the stimulus. Nonetheless, patterns of dependent activity between voxels may be lost in this averaging process, which makes the removal of breathing artifacts necessary if statistical dependence and the study of effective connectivity is the primary aim of an investigation.     

1H-MRS of the macaque monkey primary visual cortex at 7 T: strategies and pitfalls of shimming at the brain surface

Magnetic resonance spectroscopy (MRS) is ideally suited for physiology-neurochemistry experiments with the living brain and particularly for studies on the primary visual cortex (striate cortex or area V1). Yet, the highly convoluted form of the human V1 has thus far prevented the performance of MRS investigations that are spatially confined within the gray matter of this area. Typically, these studies are compromised by partial volume contaminations originating from white matter tissue, cerebrospinal fluid and other cortical areas. In this study, was exploited the relative flatness of V1 in macaques to enable single-voxel 1H-MRS from a small volume (5 x 1.6 x 5 mm3, 40 microl) that was entirely confined within the V1 gray matter of anesthetized monkeys. Linewidths of 13.5+/-1.9 Hz and 13.0+/-1.3 Hz for water and creatine, respectively, were achieved with a two-step shimming strategy for voxels at the brain surface. The quality of the obtained results paves the way for further neuroscientific research, including studies on the cortical microcircuits and the dynamic longitudinal changes occurring during cortical reorganization and plasticity.     

Multimodal integration of EEG, MEG and fMRI data for the solution of the neuroimage puzzle

In this paper, advanced methods for the modeling of human cortical activity from combined high-resolution electroencephalography (EEG), magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI) data are presented. These methods include a subject's multicompartment head model (scalp, skull, dura mater, cortex) constructed from magnetic resonance images, multidipole source model and regularized linear inverse source estimates of cortical current density. Determination of the priors in the resolution of the linear inverse problem was performed with the use of information from the hemodynamic responses of the cortical areas as revealed by block-designed (strength of activated voxels) fMRI. Examples of the application of these methods to the estimation of the time varying cortical current density activity in selected region of interest (ROI) are presented for movement-related high-resolution EEG data.     

Biophysical and neural basis of resting state functional connectivity: Evidence from non-human primates

Functional MRI (fMRI) has evolved from simple observations of regional changes in MRI signals caused by cortical activity induced by a task or stimulus, to task-free acquisitions of images in a resting state. Such resting state signals contain low frequency fluctuations which may be correlated between voxels, and strongly correlated regions are deemed to reflect functional connectivity within synchronized circuits. Resting state functional connectivity (rsFC) measures have been widely adopted by the neuroscience community, and are being used and interpreted as indicators of intrinsic neural circuits and their functional states in a broad range of applications, both basic and clinical. However, there has been relatively little work reported that validates whether inter-regional correlations in resting state fluctuations of fMRI (rsfMRI) signals actually measure functional connectivity between brain regions, or to establish how MRI data correlate with other metrics of functional connectivity. In this mini-review, we summarize recent studies of rsFC within mesoscopic scale cortical networks (100 μm–10 mm) within a well defined functional region of primary somatosensory cortex (S1), as well as spinal cord and brain white matter in non-human primates, in which we have measured spatial patterns of resting state correlations and validated their interpretation with electrophysiological signals and anatomic connections. Moreover, we emphasize that low frequency correlations are a general feature of neural systems, as evidenced by their presence in the spinal cord as well as white matter. These studies demonstrate the valuable role of high field MRI and invasive measurements in an animal model to inform the interpretation of human imaging studies.     

Characterization of cardiac-related noise in fMRI of the cervical spinal cord

Magnetic resonance imaging (MRI) has recently been applied to study spinal cord function in humans. However, spinal functional MRI (fMRI) encounters major technical challenges with cardiac noise being considered a major source of noise. The present study relied on echo-planar imaging of the cervical cord at short TR (TR=250 ms; TE=40 ms; flip=45 degrees), combined with plethysmographic recordings to characterize the spatiotemporal properties of cardiac-induced signal changes in spinal fMRI. Frequency-based analyses examining signal change at the cardiac frequency confirmed mean fluctuations of about 10% (relative to the mean signal) in the spinal cord and surrounding cerebrospinal fluid (CSF), with maximal responses reaching up to 66% in some voxels. A spatial independent component analysis (sICA) confirmed that cardiac noise is an important source of variance in spinal fMRI with several components showing a response coherent with the cardiac frequency spectrum. The time course of the main cardiac components approximated a sinusoidal function tightly coupled to the cardiac systole with at least one component showing a comparable temporal profile across runs and subjects. Spatially, both the frequency-domain analysis and the sICA demonstrated cardiac noise distributed irregularly along the full rostrocaudal extent of the segments scanned with peaks concentrated in the ventral part of the lateral slices in all scans and subjects, consistent with the major channels of CSF flow. These results confirm that cardiac-induced changes are a significant source of noise likely to affect the detection of spinal Blood Oxygen Level Dependent (BOLD) responses. Most importantly, the complex spatiotemporal structure of cardiac noise is unlikely to be accounted for adequately by ad hoc linear methods, especially in data acquired using long TR (i.e. aliasing the cardiac frequency). However, the reliable spatiotemporal distribution of cardiac noise across scanning runs and within subjects may provide a valid means to identify and extract cardiac noise based on sICA methods.     

BOLD signal and vessel dynamics: a hierarchical cluster analysis

The aim of the present study was to analyze blood oxygenation level-dependent (BOLD) signal variation during an apnea-based task in order to assess the capability of a functional magnetic resonance imaging (fMRI) procedure to estimate cerebral vascular dynamic effects. We measured BOLD contrast by hierarchical cluster analysis in healthy subjects undergoing an fMRI experiment, in which the task paradigm was one phase of inspirational apnea (IA). By processing the time courses of the fMRI experiment, analysis was performed only on a subclass of all the possible signal patterns; basically, root mean square and absolute variation differences have been calculated. Considering the baseline value obtained by computing the mean value of the initial rest period as reference, particular voxels showed relative important variations during the IA task and during the recovery phase following the IA. We focused our interest on the signal response of voxels that would correspond mainly to white and gray matter regions and that also may be affected by the proximity of large venous vessels. The results are presented as maps of space-temporal distribution of time series variations with two levels of hierarchical clustering among voxels with low to high initial response. Furthermore, we have presented a clustering of the signal response delay, conducting to a partition and identification of specified brain sites.     

Discussion on the choice of separated components in fMRI data analysis by spatial independent component analysis

By measuring the changes of magnetic resonance signals during a stimulation, the functional magnetic resonance imaging (fMRI) is able to localize the neural activation in the brain. In this report, we discuss the fMRI application of the spatial independent component analysis (spatial ICA), which maximizes statistical independence over spatial images. Included simulations show the possibility of the spatial ICA on discriminating asynchronous activations or different response patterns in an fMRI data set. An in vivo visual stimulation fMRI test was conducted, and the result shows a proper sum of the separated components as the final image is better than a single component, using fMRI data analysis by spatial ICA. Our result means that spatial ICA is a useful tool for the detection of different response activations and suggests that a proper sum of the separated independent components should be used for the imaging result of fMRI data processing.     

A SVM-based quantitative fMRI method for resting-state functional network detection

Resting-state functional magnetic resonance imaging (fMRI) aims to measure baseline neuronal connectivity independent of specific functional tasks and to capture changes in the connectivity due to neurological diseases. Most existing network detection methods rely on a fixed threshold to identify functionally connected voxels under the resting state. Due to fMRI non-stationarity, the threshold cannot adapt to variation of data characteristics across sessions and subjects, and generates unreliable mapping results. In this study, a new method is presented for resting-state fMRI data analysis. Specifically, the resting-state network mapping is formulated as an outlier detection process that is implemented using one-class support vector machine (SVM). The results are refined by using a spatial-feature domain prototype selection method and two-class SVM reclassification. The final decision on each voxel is made by comparing its probabilities of functionally connected and unconnected instead of a threshold. Multiple features for resting-state analysis were extracted and examined using an SVM-based feature selection method, and the most representative features were identified. The proposed method was evaluated using synthetic and experimental fMRI data. A comparison study was also performed with independent component analysis (ICA) and correlation analysis. The experimental results show that the proposed method can provide comparable or better network detection performance than ICA and correlation analysis. The method is potentially applicable to various resting-state quantitative fMRI studies.     

Event-related fMRI with painful electrical stimulation of the trigeminal nerve

Several functional brain imaging studies of pain using positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) have shown that painful stimulation causes activation of different brain areas. The aim of the present study was to develop and implement painful stimulation of the trigeminal nerve, which can be applied with event-related paradigms by using MRI. Twelve healthy, right-handed volunteers were examined. Painful electrical stimulation of the first trigeminal branch was performed. In an event-related setting with a 1.5 T clinical scanner with EPI capability, the following fMRI parameters were used: 20 slices, 3 mm thickness, isotropic voxel, 306 measurements with 54 randomized events. Statistical postprocessing was performed with SPM99. Activation of the ipsi- and contralateral secondary somatosensory cortex (SII), and the contralateral insular cortex was observed as well as a contralateral thalamic activation (T=4.45, extension 15 voxels). Six of the 12 volunteers revealed also activation of the cingulate cortex. The investigation demonstrates that painful stimulation of the trigeminal nerve activates the contralateral insular cortex, SII, and thalamus, as well as the ipsilateral SII. In contrast to other studies, the cingulate cortex was only activated inconsistently.     

Activation of SC during electrical stimulation of LGN: retinal antidromic stimulation or corticocollicular activation?

We have recently used combined electrostimulation, neurophysiology, microinjection and functional magnetic resonance imaging (fMRI) to study the cortical activity patterns elicited during stimulation of cortical afferents in monkeys. We found that stimulation of a site in lateral geniculate nucleus (LGN) increases the fMRI signal in the regions of primary visual cortex receiving input from that site, but suppresses it in the retinotopically matched regions of extrastriate cortex. Intracortical injection experiments showed that such suppression is due to synaptic inhibition. During these experiments, we have consistently observed activation of superior colliculus (SC) following LGN stimulation. Since LGN does not directly project to SC, the current study investigated the origin of SC activation. By examining experimental manipulations inactivating the primary visual cortex, we present here evidence that the robust SC activation, which follows the stimulation of LGN, is due to the activation of corticocollicular pathway.     

Dissecting cognitive stages with time-resolved fMRI data: a comparison of fuzzy clustering and independent component analysis

In combination with cognitive tasks entailing sequences of sensory and cognitive processes, event-related acquisition schemes allow using functional MRI to examine not only the topography but also the temporal sequence of cortical activation across brain regions (time-resolved fMRI). In this study, we compared two data-driven methods--fuzzy clustering method (FCM) and independent component analysis (ICA)--in the context of time-resolved fMRI data collected during the performance of a newly devised visual imagery task. We analyzed a multisubject fMRI data set using both methods and compared their results in terms of within- and between-subject consistency and spatial and temporal correspondence of obtained maps and time courses. Both FCM and spatial ICA allowed discriminating the contribution of distinct networks of brain regions to the main cognitive stages of the task (auditory perception, mental imagery and behavioural response), with good agreement across methods. Whereas ICA worked optimally on the original time series, averaging with respect to the task onset (and thus introducing some a priori information on the stimulation protocol) was found to be indispensable in the case of FCM. On averaged time series, FCM led to a richer decomposition of the spatio-temporal patterns of activation and allowed a finer separation of the neurocognitive processes subserving the mental imagery task. This study confirms the efficacy of the two examined methods in the data-driven estimation of hemodynamic responses in time-resolved fMRI studies and provides empirical guidelines to their use.     

A modified fuzzy clustering algorithm for operator independent brain tissue classification of dual echo MR images.

Methods for brain tissue classification or segmentation of structural magnetic resonance imaging (MRI) data should ideally be independent of human operators for reasons of reliability and tractability. An algorithm is described for fully automated segmentation of dual echo, fast spin-echo MRI data. The method is used to assign fuzzy-membership values for each of four tissue classes (gray matter, white matter, cerebrospinal fluid and dura) to each voxel based on partition of a two dimensional feature space. Fuzzy clustering is modified for this application in two ways. First, a two component normal mixture model is initially fitted to the thresholded feature space to identify exemplary gray and white matter voxels. These exemplary data protect subsequently estimated cluster means against the tendency of unmodified fuzzy clustering to equalize the number of voxels in each class. Second, fuzzy clustering is implemented in a moving window scheme that accommodates reduced image contrast at the axial extremes of the transmitting/receiving coil. MRI data acquired from 5 normal volunteers were used to identify stable values for three arbitrary parameters of the algorithm: feature space threshold, relative weight of exemplary gray and white matter voxels, and moving window size. The modified algorithm incorporating these parameter values was then used to classify data from simulated images of the brain, validating the use of fuzzy-membership values as estimates of partial volume. Gray:white matter ratios were estimated from 20 twenty normal volunteers (mean age 32.8 years). Processing time for each three-dimensional image was approximately 30 min on a 170 MHz workstation. Mean cerebral gray and white matter volumes estimated from these automatically segmented images were very similar to comparable results previously obtained by operator dependent methods, but without their inherent unreliability.     

Validating the performance of one-time decomposition for fMRI analysis using ICA with automatic target generation process

Independent component analysis (ICA) has been proven to be effective for functional magnetic resonance imaging (fMRI) data analysis. However, ICA decomposition requires to optimize the unmixing matrix iteratively whose initial values are generated randomly. Thus the randomness of the initialization leads to different ICA decomposition results. Therefore, just one-time decomposition for fMRI data analysis is not usually reliable. Under this circumstance, several methods about repeated decompositions with ICA (RDICA) were proposed to reveal the stability of ICA decomposition. Although utilizing RDICA has achieved satisfying results in validating the performance of ICA decomposition, RDICA cost much computing time. To mitigate the problem, in this paper, we propose a method, named ATGP-ICA, to do the fMRI data analysis. This method generates fixed initial values with automatic target generation process (ATGP) instead of being produced randomly. We performed experimental tests on both hybrid data and fMRI data to indicate the effectiveness of the new method and made a performance comparison of the traditional one-time decomposition with ICA (ODICA), RDICA and ATGP-ICA. The proposed method demonstrated that it not only could eliminate the randomness of ICA decomposition, but also could save much computing time compared to RDICA. Furthermore, the ROC (Receiver Operating Characteristic) power analysis also denoted the better signal reconstruction performance of ATGP-ICA than that of RDICA.