Detecting cortical activities from fMRI time-course data using the MUSIC algorithm with forward and backward covariance averaging

New Processing Methods in Functional MRI

Two processing methods of fMRI data are proposed: vector orthogonalization and Fisher transformation of correlation coefficients (cc) distribution.

The former is based on orthogonalization of vectors V (time course of signal intensity) and R (noise) to make V independent from R.

The latter is based on Fisher transformation of cc distribution. From this distribution, by usual statistical tests, it is possible to detect the values of the cc that are significantly different from the mean in order to select activated pixels.

Optimal compressed sensing reconstructions of fMRI using 2D deterministic and stochastic sampling geometries

BACKGROUND

Compressive sensing can provide a promising framework for accelerating fMRI image acquisition by allowing reconstructions from a limited number of frequency-domain samples. Unfortunately, the majority of compressive sensing studies are based on stochastic sampling geometries that cannot guarantee fast acquisitions that are needed for fMRI. The purpose of this study is to provide a comprehensive optimization framework that can be used to determine the optimal 2D stochastic or deterministic sampling geometry, as well as to provide optimal reconstruction parameter values for guaranteeing image quality in the reconstructed images.

METHODS

We investigate the use of frequency-space (k-space) sampling based on: (i) 2D deterministic geometries of dyadic phase encoding (DPE) and spiral low pass (SLP) geometries, and (ii) 2D stochastic geometries based on random phase encoding (RPE) and random samples on a PDF (RSP). Overall, we consider over 36 frequency-sampling geometries at different sampling rates. For each geometry, we compute optimal reconstructions of single BOLD fMRI ON & OFF images, as well as BOLD fMRI activity maps based on the difference between the ON and OFF images. We also provide an optimization framework for determining the optimal parameters and sampling geometry prior to scanning.

RESULTS

For each geometry, we show that reconstruction parameter optimization converged after just a few iterations. Parameter optimization led to significant image quality improvements. For activity detection, retaining only 20.3% of the samples using SLP gave a mean PSNR value of 57.58 dB. We also validated this result with the use of the Structural Similarity Index Matrix (SSIM) image quality metric. SSIM gave an excellent mean value of 0.9747 (max = 1). This indicates that excellent reconstruction results can be achieved. Median parameter values also gave excellent reconstruction results for the ON/OFF images using the SLP sampling geometry (mean SSIM > =0.93). Here, median parameter values were obtained using mean-SSIM optimization. This approach was also validated using leave-one-out.

CONCLUSIONS

We have found that compressive sensing parameter optimization can dramatically improve fMRI image reconstruction quality. Furthermore, 2D MRI scanning based on the SLP geometries consistently gave the best image reconstruction results. The implication of this result is that less complex sampling geometries will suffice over random sampling. We have also found that we can obtain stable parameter regions that can be used to achieve specific levels of image reconstruction quality when combined with specific k-space sampling geometries. Furthermore, median parameter values can be used to obtain excellent reconstruction results.

Functional magnetic resonance inverse imaging of human visuomotor systems using eigenspace linearly constrained minimum amplitude (eLCMA) beamformer

Recently proposed dynamic magnetic resonance (MR) inverse imaging (InI) is a novel parallel imaging reconstruction technique capable of improving the temporal resolution of blood-oxygen level-dependent (BOLD) contrast functional MRI (fMRI) to the order of milliseconds at the cost of moderate spatial resolution. Volumetric InI reconstructs spatial information from projection data by solving ill-posed inverse problems using simultaneous acquisitions from a RF coil array. Previously a spatial filtering technique based on linearly constrained minimum variance (LCMV) beamformer was suggested to localize the hemodynamic changes of dynamic InI data with improved spatial resolution and sensitivity. Here we report an advancement of the spatial filtering method, which combines the eigenspace projection of the measured data and the L1-norm minimization of the spatial filters' output noise amplitude, to further improve the detection power of BOLD contrast fMRI data. Using numerical simulation and in vivo data, we demonstrate that this eigenspace linearly constrained minimum amplitude (eLCMA) beamformer can reconstruct spatiotemporal hemodynamic signals with high statistical significance values and high spatial resolution in event-related two-choice reaction time visuomotor experiments.

Partially adaptive STAP algorithm approaches to functional MRI

In this paper, the architectures of three partially adaptive space-time adaptive processing (STAP) algorithms are introduced, one of which is explored in detail, that reduce dimensionality and improve tractability over fully adaptive STAP when used in the construction of brain activation maps in functional magnetic resonance imaging (fMRI). Computer simulations incorporating actual MRI noise and human data analysis indicate that element space partially adaptive STAP can attain close to the performance of fully adaptive STAP while significantly decreasing processing time and maximum memory requirements, and thus demonstrates potential in fMRI analysis.

Delay correlation subspace decomposition algorithm and its application in fMRI

This paper reports a new delay subspace decomposition (DSD) algorithm. Instead of using the canonical zero-delay correlation matrix, the new DSD algorithm introduces a delay into the correlation matrix of the subspace decomposition to suppress noises in the data. The algorithm is applied to functional magnetic resonance imaging (fMRI) to detect the regions of focal activities in the brain. The efficiency is evaluated by comparing with independent component analysis and principal component analysis method of fMRI.

The concept of 'developing the brain': a new natural science for learning and education

From the viewpoint of biology, learning and education can be defined as the processes of forming neuronal connections in response to external environmental stimuli, and of controlling or adding appropriate stimuli, respectively. Learning and education can thus be studied as a new field of natural sciences with the entire human life span as its subject, thus including various problems such as fetal environment, childcare, language acquisition, general/special education, and rehabilitation. Non-invasive imaging of higher-order brain functions in humans will clarify the brain's developmental processes, and will provide various evidence for learning sciences. This new approach is called 'developing the brain' or 'brain science and education'. The origin of the concept and its present state are described and its future prospects are briefly analyzed.

A STAP algorithm approach to fMRI: a simulation study

PURPOSE

To adapt the space-time adaptive processing (STAP) algorithm, previously developed in the field of sensor array processing and applied to radar signal processing, for use in construction of brain activation maps in functional magnetic resonance imaging (fMRI).

MATERIALS AND METHODS

STAP is a two-dimensional filter in which both the spatial and temporal responses are controlled adaptively. It processes space-time data as a complete spatiotemporal set. Unlike presently used fMRI techniques, STAP locates activated regions both spatially and in frequency.

RESULTS

Computer simulations incorporating actual MRI noise indicate that STAP exhibits a high degree of accuracy in detecting the small signal intensity changes inherent in fMRI.

CONCLUSION

Because STAP processes space-time data as a single data matrix, it exhibits potential over currently available fMRI methods in providing a measure of the full spatiotemporal extent of a task-related activity.

Localization of fluorescence spots with space-space MUSIC for mammographylike measurement systems

Breast cancer diagnosis may be improved by optical fluorescence imaging techniques in the near-infrared wavelength range. We have shown that the recently proposed space-space MUSIC (multiple signal classification) algorithm allows the 3-D localization of focal fluorophore-tagged lesions in a turbid medium from 2-D fluorescence data obtained from laser excitations at different positions. The data are assumed to be measured with two parallel planar sensor arrays on the top and bottom of the medium. The laser sources are integrated at different positions in one of the planes. The space-space data are arranged into an MxN matrix (M, number of sensors; N, number of excitation sources). A singular-value decomposition (SVD) of this matrix yields the detectable number of spot regions with linearly independent behavior with respect to the laser excitation positions and thus allows definition of a signal subspace. Matches between this signal subspace and data from model spots are tested at scanned points in a model medium viewed as the breast region under study. The locations of best matches are then considered the centers of gravity of focal lesions. The optical model used was unbounded and optically homogeneous. Nevertheless, simulated spots in bounded, inhomogeneous media modeling the breast could be localized accurately.

Towards virtual electrical breast biopsy: space-frequency MUSIC for trans-admittance data

Breast cancer diagnosis may be improved by electrical immittance measurements. We have developed a novel method, space-frequency MUltiple Signal Classification (MUSIC), to determine three-dimensional positions and electrical parameters of focal lesions from multifrequency trans-admittance data recorded with a planar electrode array. A homogeneous infinite volume conductor containing focal inhomogeneities proved to be a useful patient-independent model for the breast containing focal lesions. Lesions polarized through the externally applied electric field are considered as distributions of aligned dipoles. Independence of the lesions' shape and size is achieved by a multipole expansion of such a dipole distribution. Thus, lesions are described by point-like multipoles. Their admittance contributions are given by a sum over products of multipole-specific source-sensor transfer functions, called lead fields, multiplied by their moments. Lesion localization corresponds to multipole search, and uses orthonormalized lead fields for comparison with a signal subspace from a singular value analysis of a space-frequency data matrix. At the locations found, the moments' frequency behavior is calculated which is assumed to be tissue-specific due to their dependence on conductivities. Results from clinical data show that space-frequency MUSIC successfully localizes lesions. Tissue differentiation might be possible, especially when the frequency range of the measurement system will be increased.

Generalized likelihood ratio detection for fMRI using complex data

The majority of functional magnetic resonance imaging (fMRI) studies obtain functional information using statistical tests based on the magnitude image reconstructions. Recently, a complex correlation (CC) test was proposed based on the complex image data in order to take advantage of phase information in the signal. However, the CC test ignores additional phase information in the baseline component of the data. In this paper, a new detector for fMRI based on a generalized likelihood ratio test (GLRT) is proposed. The GLRT exploits the fact that the fMRI response signal as well as the baseline component of the data share a common phase. Theoretical analysis and Monte Carlo simulation are used to explore the performance of the new detector. At relatively low signal intensities, the GLRT outperforms both the standard magnitude data test and the CC test. At high signal intensities, the GLRT performs as well as the standard magnitude data test and significantly better than the CC test.

Spatio-temporal fMRI analysis using Markov random fields

Functional magnetic resonance images (fMRI's) provide high-resolution datasets which allow researchers to obtain accurate delineation and sensitive detection of activation areas involved in cognitive processes. To preserve the resolution of this noninvasive technique, refined methods are required in the analysis of the data. In this paper, we first discuss the widely used methods based on a statistical parameter map (SPM) analysis exposing the different shortcomings of this approach when considering high-resolution data. First, the often used Gaussian filtering results in a blurring effect and in delocalization of the activated area. Secondly, the SPM approach only considers false alarms due to noise but not rejections of activated voxels. We propose to embed the fMRI analysis problem into a Bayesian framework consisting of two steps: i) data restoration and ii) data analysis. We, therefore, propose two Markov random fields (MRF's) to solve these two problems. Results on three protocols (visual, motor and word recognition) are shown for two SPM approaches and compared with the proposed MRF approach.