Convolution Power Spectrum Analysis for fMRI Data Based on Prior Image Signal

Functional MRI (fMRI) data-processing methods based on changes in the time domain involve, among other things, correlation analysis and use of the general linear model with statistical parametric mapping (SPM). Unlike conventional fMRI data analysis methods, which aim to model the blood-oxygen-level-dependent (BOLD) response of voxels as a function of time, the theory of power spectrum (PS) analysis focuses completely on understanding the dynamic energy change of interacting systems. We propose a new convolution PS (CPS) analysis of fMRI data, based on the theory of matched filtering, to detect brain functional activation for fMRI data. First, convolution signals are computed between the measured fMRI signals and the image signal of prior experimental pattern to suppress noise in the fMRI data. Then, the PS density analysis of the convolution signal is specified as the quantitative analysis energy index of BOLD signal change. The data from simulation studies and in vivo fMRI studies, including block-design experiments, reveal that the CPS method enables a more effective detection of some aspects of brain functional activation, as compared with the canonical PS SPM and the support vector machine methods. Our results demonstrate that the CPS method is useful as a complementary analysis in revealing brain functional information regarding the complex nature of fMRI time series.      

A sparse Bayesian method for determination of flexible design matrix for fMRI data analysis

The construction of a design matrix is critical to the accurate detection of activation regions of the brain in functional magnetic resonance imaging (fMRI). The design matrix should be flexible to capture the unknown slowly varying drifts as well as robust enough to avoid overfitting. In this paper, a sparse Bayesian learning method is proposed to determine a suitable design matrix for fMRI data analysis. Based on a generalized linear model, this learning method lets the data itself determine the form of the regressors in the design matrix. It automatically finds those regressors that are relevant to the generation of the fMRI data and discards the others that are irrelevant. The proposed approach integrates the advantages of currently employed methods of fMRI data analysis (the model-driven and the data-driven methods). Results from the simulation studies clearly reveal the superiority of the proposed scheme to the conventional t-test method of fMRI data analysis.     

BOLD contrast and noise characteristics of densely sampled multi-echo fMRI data

Blood oxygenation level dependent (BOLD) contrast in functional magnetic resonance imaging (fMRI) can be enhanced using multi-echo imaging and postprocessing techniques that combine the echoes in weighted summation. Here, existing echo-weighting methods are reassessed in the context of an explicit physiological noise model, and a new method is introduced: weights that scale linearly with echo time. Additionally, a method using data-driven weights defined using principal component analysis (PCA) is included for comparison. Differences in BOLD contrast enhancement between methods were compared analytically where possible, and using Monte Carlo simulations for different noise conditions and different combinations of acquisition parameters. The comparisons were also validated through densely sampled (256-echo) multi-echo fMRI experimental data acquired at 1.5T and 3.0T. Results indicated that the contrast-to-noise ratio (CNR) of the studied weighting methods have a strong dependence on the physiological noise, echo spacing and the width of the sampling window. With low noise correlations between echoes, contrast gain for all weighting methods was shown to have a square root dependence on the echo sampling density, and in typical experimental noise conditions, increasing the sampling window beyond 3·T2* produced marginal additional benefit. Simulations and experiments also emphasized that noise correlations between echoes are likely the main factor limiting the potential CNR gains achievable by densely sampled multi-echo fMRI.     

An integrated neighborhood correlation and hierarchical clustering approach of functional MRI

Clustering analysis is a promising data-driven method for the analysis of functional magnetic resonance imaging (fMRI) time series, however, the huge computation load makes it difficult for practical use. In this paper, neighborhood correlation (NC) and hierarchical clustering (HC) methods are integrated as a new approach where fMRI data are processed first by NC to get a preliminary image of brain activations, and then by HC to remove some noises. In HC, to better use spatial and temporal information in fMRI data, a new spatio-temporal measure is introduced. A simulation study and an application to visual fMRI data show that the brain activations can be effectively detected and that different response patterns can be discriminated. These results suggest that the proposed new integrated approach could be useful in detecting weak fMRI signals.     

A computational multiresolution BOLD fMRI model

Blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) is a widely used method for brain mapping. BOLD fMRI signal detection is based on an intravoxel dephasing mechanism. This model involves bulk nuclear spin precession in a BOLD-induced inhomogeneous magnetic field within a millimeter-resolution voxel, that is, BOLD signal formation spans a huge spatial scale range from Angstrom to millimeter. In this letter, we present a computational model for multiresolution BOLD fMRI simulation, which consists of partitioning the nuclear spin pool into spin packets at a mesoscopic scale (～10(-6) m), and calculating multiresolution voxel signals by grouping spin packets at a macroscopic scale range (10(-5) to 10(-3) m). Under a small-angle approximation, we find that the BOLD signal intensity is related to its phase counterpart (or BOLD fieldmap) across two spatial resolution levels.     

Signal nonlinearity in fMRI: a comparison between BOLD and MION

In this paper, we introduce a methodology for comparing the nonlinearities present in sets of time series using four different nonlinearity measures, one of which, the "delay vector variance" method, is a novel approach to the characterization of a time series. It is then applied to examine the difference in nonlinearity between functional magnetic resonance imaging (fMRI) signals that have been recorded using different contrast agents. Recently, an exogenous contrast agent, monocrystalline iron oxide particle (MION), has been introduced for fMRI, which has been shown to increase the functional sensitivity compared with the traditional blood oxygen level dependent (BOLD) technique. The resulting fMRI signals are influenced by cerebral blood volume, whereas the more traditionally recorded BOLD signals are influenced not only by cerebral blood volume, but also by the cerebral blood flow and the metabolic rate of oxygen. The proposed methodology is applied to address the question whether this difference in the number of physiological variables is reflected in a difference in the degree of nonlinearity. We therefore analyze two sets of fMRI signals, one from a BOLD and the other from a MION monkey study with similar experimental designs. In the neuroimaging context, the proposed nonlinearity analyses are different from those described in the literature, since no a priori model is assumed: rather than pinpointing the source(s) of nonlinearity, nonparametric analyses are performed on BOLD and MION fMRI signals. Furthermore, we introduce a strategy for analyzing a population of fMRI signals, rather than focusing the analysis on one signal, as is traditionally done in the domain of nonlinear signal processing. Our results show that, overall, the BOLD signals are more nonlinear in nature than the MION ones, which is in agreement with current hypotheses.     

Selection criteria for the analysis of data-driven clusters in cerebral FMRI

Functional MRI (fMRI) may be possible without a priori models of the cerebral hemodynamic response. First, such data-driven fMRI requires that all cerebral territories with distinct patterns be identified. Second, a systematic selection method is necessary to prevent the subjective interpretation of the identified territories. This paper addresses the second point by proposing a novel method for the automated interpretation of identified territories in data-driven fMRI. Selection criteria are formulated using: 1) the temporal cross-correlation between each identified territory and the paradigm and 2) the spatial contiguity of the corresponding voxel map. Ten event-design fMRI data sets are analyzed with one prominent algorithm, fuzzy c-means clustering, before applying the selection criteria. For comparison, these data are also analyzed with an established, model-based method: statistical parametric mapping. Both methods produced similar results and identified potential activation in the expected territory of the sensorimotor cortex in all ten data sets. Moreover, the proposed method classified distinct territories in separate clusters. Selected clusters have a mean temporal correlation coefficient of 0.39+/-0.07 (n=19) with a mean 2.7+/-1.4 second response delay. At most, four separate contiguous territories were observed in 87% of these clusters. These results suggest that the proposed method may be effective for exploratory fMRI studies where the hemodynamic response is perturbed during cerebrovascular disease.     

Estimation of the hemodynamic response of fMRI Data using RBF neural network

Functional magnetic resonance imaging (fMRI) is an important technique for neuroimaging. The conventional system identification methods used in fMRI data analysis assume a linear time-invariant system with the impulse response described by the hemodynamic responses (HDR). However, the measured blood oxygenation level-dependent (BOLD) signals to a particular processing task (for example, rapid event-related fMRI design) show nonlinear properties and vary with different brain regions and subjects. In this paper, radial basis function (RBF) neural network (a powerful technique for modelling nonlinearities) is proposed to model the dynamics underlying the fMRI data. The equivalence of the proposed method to the existing Volterra series method has been demonstrated. It is shown that the first- and second-order Volterra kernels could be deduced from the parameters of the RBF neural network. Studies on both simulated (using Balloon model) as well as real event-related fMRI data show that the proposed method can accurately estimate the HDR of the brain and capture the variations of the HDRs as a function of the brain regions and subjects.     

Clustered components analysis for functional MRI

A common method of increasing hemodynamic response (SNR) in functional magnetic resonance imaging (fMRI) is to average signal timecourses across voxels. This technique is potentially problematic because the hemodynamic response may vary across the brain. Such averaging may destroy significant features in the temporal evolution of the fMRI response that stem from either differences in vascular coupling to neural tissue or actual differences in the neural response between two averaged voxels. Two novel techniques are presented in this paper in order to aid in an improved SNR estimate of the hemodynamic response while preserving statistically significant voxel-wise differences. The first technique is signal subspace estimation for periodic stimulus paradigms that involves a simple thresholding method. This increases SNR via dimensionality reduction. The second technique that we call clustered components analysis is a novel amplitude-independent clustering method based upon an explicit statistical data model. It includes an unsupervised method for estimating the number of clusters. Our methods are applied to simulated data for verification and comparison to other techniques. A human experiment was also designed to stimulate different functional cortices. Our methods separated hemodynamic response signals into clusters that tended to be classified according to tissue characteristics.     

fMRI-based hierarchical SVM model for the classification and grading of liver fibrosis

We present a novel method for the automatic classification and grading of liver fibrosis based on hepatic hemodynamic changes measured noninvasively from functional MRI (fMRI) scans combined with hypercapnia and hyperoxia. The supervised learning method automatically creates a classification and grading model for liver fibrosis grade from training datasets. It constructs a statistical model of liver fibrosis by evaluating the signal intensity time course and local variance in T2(*)-W fMRI scans acquired during the breathing of air, air-carbon dioxide, and carbogen with a hierarchical multiclass binary-based support vector machine (SVM) classifier. Two experimental studies on 162 slices from 34 mice with the hierarchical multiclass binary-based SVM classifier yield 96.9% separation accuracy between healthy and histological-based fibrosis graded subjects, and an overall accuracy of 75.3% for healthy, fibrotic, and cirrhotic subjects. These results outperform existing image-based methods that can discriminate between healthy and mild-grade fibrosis subjects.     

Analysis of FMRI data using an integrated principal component analysis and supervised affinity propagation clustering approach

Clustering analysis is a promising data-driven method for analyzing functional magnetic resonance imaging (fMRI) time series data. The huge computational load, however, creates practical difficulties for this technique. We present a novel approach, integrating principal component analysis (PCA) and supervised affinity propagation clustering (SAPC). In this method, fMRI data are initially processed by PCA to obtain a preliminary image of brain activation. SAPC is then used to detect different brain functional activation patterns. We used a supervised Silhouette index to optimize clustering quality and automatically search for the optimal parameter p in SAPC, so that the basic affinity propagation clustering is improved by applying SAPC. Four simulation studies and tests with three in vivo fMRI datasets containing data from both block-design and event-related experiments revealed that functional brain activation was effectively detected and different response patterns were distinguished using our integrated method. In addition, the improved SAPC method was superior to the k -centers clustering and hierarchical clustering methods in both block-design and event-related fMRI data, as measured by the average squared error. These results suggest that our proposed novel integrated approach will be useful for detecting brain functional activation in both block-design and event-related experimental fMRI data.     

Activelets: Wavelets for sparse representation of hemodynamic responses

We propose a new framework to extract the activity-related component in the BOLD functional magnetic resonance imaging (fMRI) signal. As opposed to traditional fMRI signal analysis techniques, we do not impose any prior knowledge of the event timing. Instead, our basic assumption is that the activation pattern is a sequence of short and sparsely distributed stimuli, as is the case in slow event-related fMRI.We introduce new wavelet bases, termed “activelets”, which sparsify the activity-related BOLD signal. These wavelets mimic the behavior of the differential operator underlying the hemodynamic system. To recover the sparse representation, we deploy a sparse-solution search algorithm.The feasibility of the method is evaluated using both synthetic and experimental fMRI data. The importance of the activelet basis and the non-linear sparse recovery algorithm is demonstrated by comparison against classical B-spline wavelets and linear regularization, respectively.     

Pareto-Optimal Methods for Gene Ranking

The massive scale and variability of microarray gene data creates new and challenging problems of signal extraction, gene clustering, and data mining, especially for temporal gene profiles. Many data mining methods for finding interesting gene expression patterns are based on thresholding single discriminants, e.g. the ratio of between-class to within-class variation or correlation to a template. Here a different approach is introduced for extracting information from gene microarrays. The approach is based on multiple objective optimization and we call it Pareto front analysis (PFA). This method establishes a ranking of genes according to estimated probabilities that each gene is Pareto-optimal, i.e., that it lies on the Pareto front of the multiple objective scattergram. Both a model-driven Bayesian Pareto method and a data-driven non-parametric Pareto method, based on rank-order statistics, are presented. The methods are illustrated for two gene microarray experiments.     

Unsupervised learning and mapping of active brain functional MRI signals based on hidden semi-Markov event sequence models

In this paper, a novel functional magnetic resonance imaging (fMRI) brain mapping method is presented within the statistical modeling framework of hidden semi-Markov event sequence models (HSMESMs). Neural activation detection is formulated at the voxel level in terms of time coupling between the sequence of hemodynamic response onsets (HROs) observed in the fMRI signal, and an HSMESM of the hidden sequence of task-induced neural activations. The sequence of HRO events is derived from a continuous wavelet transform (CWT) of the fMRI signal. The brain activation HSMESM is built from the timing information of the input stimulation protocol. The rich mathematical framework of HSMESMs makes these models an effective and versatile approach for fMRI data analysis. Solving for the HSMESM Evaluation and Learning problems enables the model to automatically detect neural activation embedded in a given set of fMRI signals, without requiring any template basis function or prior shape assumption for the fMRI response. Solving for the HSMESM Decoding problem allows to enrich brain mapping with activation lag mapping, activation mode visualizing, and hemodynamic response function analysis. Activation detection results obtained on synthetic and real epoch-related fMRI data demonstrate the superiority of the HSMESM mapping method with respect to a real application case of the statistical parametric mapping (SPM) approach. In addition, the HSMESM mapping method appears clearly insensitive to timing variations of the hemodynamic response, and exhibits low sensitivity to fluctuations of its shape.     

Adaptive denoising of event-related functional magnetic resonance imaging data using spectral subtraction

A new adaptive signal-preserving technique for noise suppression in event-related functional magnetic resonance imaging (fMRI) data is proposed based on spectral subtraction. The proposed technique estimates a parametric model for the power spectrum of random noise from the acquired data based on the characteristics of the Rician statistical model. This model is subsequently used to estimate a noise-suppressed power spectrum for any given pixel time course by simple subtraction of power spectra. The new technique is tested using computer simulations and real data from event-related fMRI experiments. The results show the potential of the new technique in suppressing noise while preserving the other deterministic components in the signal. Moreover, we demonstrate that further analysis using principal component analysis and independent component analysis shows a significant improvement in both convergence and clarity of results when the new technique is used. Given its simple form, the new method does not change the statistical characteristics of the signal or cause correlated noise to be present in the processed signal. This suggests the value of the new technique as a useful preprocessing step for fMRI data analysis.     

A new method for the extraction of fetal ECG from the composite abdominal signal

We developed a wavelet transform-based method to extract the fetal electrocardiogram (ECG) from the composite abdominal signal. This is based on the detection of the singularities obtained from the composite abdominal signal, using the modulus maxima in the wavelet domain. Modulus maxima locations of the abdominal signal are used to discriminate between maternal and fetal ECG signals. Two different approaches have been considered. In the first approach, at least one thoracic signal is used as the a prior to perform the classification whereas in the second approach no thoracic signal is needed. A reconstruction method is utilized to obtain the fetal ECG signal from the detected fetal modulus maxima. The proposed technique is different from the classical time-domain methods, in that we exploit the most distinct features of the signal, leading to more robustness with respect to signal perturbations. Results of experiments with both synthetic and real ECG data have been presented to demonstrate the efficacy of the proposed method.     

多基地雷达聚类分析鉴别有源假目标

针对现有多基地雷达抗欺骗式干扰方法无法应用于多干扰源的问题,该文提出一种基于聚类分析的多基地雷达鉴别有源假目标方法,利用真假目标接收信号矢量之间相关性的差异,以相关系数为度量,通过聚类分析方法,将相同干扰源产生的假目标聚为一类,每个真实目标各为一类,实现有源假目标的有效鉴别。该方法可用于鉴别任意欺骗调制方式产生的有源假目标,且适用于多个干扰源实施分布式干扰的应用场景。最后,通过仿真实验,验证了所提聚类分析方法鉴别有源假目标的有效性。     

非线性脑区相关性分析及动态脑网络构建方法

针对静息态脑功能磁共振的血氧依赖水平信号中的非线性特征,在基于滑动窗口的动态数据分析技术的基础上,本文重点对构建全脑动态特征矩阵过程中的不同非线性相关分析方法展开了对比研究,并给出了构建脑网络中的阈值确定方法。脑网络降维和状态聚类实验结果显示,在阈值参数选择合理的前提下,采用三种非线性分析方法对BOLD信号进行的相关分析均可得到结构规模相似的脑网络,并且其状态转换结果均显现出相似的规律性,从而为下一步展开脑网络的动态特性分析和演化过程研究奠定了基础。      

A generalization of the two-dimensional prolate spheroidal wave function method for nonrectilinear MRI data acquisition methods.

The two-dimensional (2-D) prolate spheroidal wave function (2-D PSWF) method was previously introduced as an efficient method for trading off between spatial and temporal resolution in magnetic resonance imaging (MRI), with minimal penalty due to truncation and partial volume effects. In the 2-D PSWF method, the k-space sampling area and a matching 2-D PSWF filter, with optimal signal concentration and minimal truncation artifacts, are determined by the shape and size of a given convex region of interest (ROI). The spatial information in the reduced k-space data is used to calculate the total image intensity over a nonsquare ROI instead of producing a low-resolution image. This method can be used for tracking dynamic signals from non-square ROIs using a reduced k-space sampling area, while achieving minimal signal leakage. However, the previous theory is limited to the case of rectilinear sampling. In order to make the 2-D PSWF method more suitable for dynamic studies, this paper presents a generalized version of the 2-D PSWF theory that can be applied to nonrectilinear data acquisition methods. The method is applied to an fMRI study using a spiral trajectory, which illustrates the methods efficiency at tracking hemodynamic signals with high temporal resolution.