In functional magnetic resonance imaging (fMRI), it is important to observe the functioning brain as fast as possible and at as high of a spatial resolution as possible. Increased spatial and temporal speed results in voxels with increased noise relative to signal and contrast. There is much evidence to suggest that there is important biological information contained within the phase component of the fMRI signal. When the signal-to-noise ratio within a voxel is low, as when there is ultra-high resolution, the marginal statistical distribution of the phase is non-standard and difficult to work with. This non-standard marginal phase distribution at high signal-to-noise ratios is Normally distributed, but at low signal-to-noise ratios needs to be utilized for accurate modeling. In this work, phase-only activation will be computed directly from Lathi’s mathematically correct non-Normal distribution, yielding additional physiological information to what is typically observed.

Functional Magnetic Resonance Imaging (fMRI) enables researchers to study brain function and advance understanding in human sciences. Spatial and temporal changes in brain metabolism as by detecting the Blood Oxygen Level Dependent (BOLD) contrast signal are represented in the frequency domain of an image, known as k-space. Traditional MRI methodologies require full k-space information, which follows a unique data acquisition sequence to reconstruct the complete image. This process presents a time-consuming obstacle for medical imaging techniques. Our study proposes a novel image reconstruction method to enhance the efficiency of data acquisition while maintaining high accuracy in activation detection. The through-plane and in-plane acceleration techniques are combined to accelerate image acquisition along two dimensions. Multiple image-shift strategies and a 2D Hadamard encoding scheme are used to increase encoding diversity and reduce slice leakage. By applying our approach to both simulated and experimental fMRI data, we successfully reduced total scan time while achieving a higher signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) in regions of interest (ROI). Compared with conventional reconstruction strategies, the proposed method demonstrates potential improvements in activation detection under specific acceleration and encoding conditions, while also providing voxel-wise estimates through a Bayesian framework.

Electroanatomical mapping is a technique used in cardiology to create a detailed 3D map of the electrical activity in the heart. It is useful for diagnosis, treatment planning and real time guidance in cardiac ablation procedures to treat arrhythmias like atrial fibrillation. A probabilistic machine learning model trained on a library of CT/MRI scans of the heart can be used during electroanatomical mapping to generate a patient-specific 3D model of the chamber being mapped. The use of probabilistic machine learning models under a Bayesian framework provides a way to quantify uncertainty in results and provide a natural framework of interpretability of the model. Here we introduce a Bayesian approach to surface reconstruction of cardiac chamber models from a sparse 3D point cloud data acquired during electroanatomical mapping. We show how probabilistic graphical models trained on segmented CT/MRI data can be used to generate cardiac chamber models from few acquired locations thereby reducing procedure time and x-ray exposure. We show how they provide insight into what the neural network learns from the segmented CT/MRI images used to train the network, which provides explainability to the resulting cardiac chamber models generated by the model.

Functional magnetic resonance imaging (fMRI) data generally consist of time series image volumes of the magnitude of complex-valued observations at each voxel. However, incorporating Gaussian-based time series models and the Rice distribution-a more accurate model for the data-in the time series have been separated by a distributional "mismatch." We bridge this gap by including pth-order autoregressive (AR) errors into the Gaussian model for the latent real and imaginary components underlying the Rice-distributed magnitude data. Parameter estimation is then done by augmenting the observed magnitude data with the missing phase data in an expectation-maximization (EM) algorithm framework and followed by AR order determination and computation of test statistics for activation detection. Using simulated and experimental low-SNR fMRI data, we compare the performance of this Ricean time series model with a Gaussian AR(p) model for the magnitude data and also with a complex Gaussian time series model for the entire complex-valued data. Our results show improved parameter estimation and activation detection under the Ricean AR(p) model for the magnitude data than its Gaussian counterpart. The model using the complex-valued data (which is rarely collected in practice) detects activation better than both magnitude-only models but only because it has more data. Thus, while our results here provide for the improved analysis of commonly-collected and archived magnitude-only fMRI datasets, they also argue strongly against the currently routine practice of discarding the phase of the complex-valued fMRI time series, advocating instead for their inclusion in the analysis.

In fMRI, capturing brain activation during a task is dependent on how quickly k-space arrays are obtained. Acquiring full k-space arrays, which are reconstructed into images using the inverse Fourier transform (IFT), that make up volume images can take a considerable amount of scan time. Under-sampling k-space reduces the acquisition time, but results in aliased, or "folded," images. GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) is a parallel imaging technique that yields full images from subsampled arrays of k-space. GRAPPA uses localized interpolation weights, which are estimated per-scan and fixed over time, to fill in the missing spatial frequencies of the subsampled k-space. Hence, we propose a Bayesian approach to GRAPPA (BGRAPPA) where space measurement uncertainty are assessed from the a priori calibration k-space arrays. The prior information is utilized to estimate the missing spatial frequency values from the posterior distribution and reconstruct into full field-of-view images. Our BGRAPPA technique successfully reconstructed both a simulated and experimental single slice image with less artifacts, reduced noise leading to an increased signal-to-noise ratio (SNR), and stronger power of task detection.

FMRI has been a safe medical imaging tool to study brain function by demonstrating the spatial and temporal changes in brain metabolism in recent decades. To capture brain functionality more efficiently, efforts focus on accelerating image acquisition acquired per unit of time that create each volume image without losing full anatomical structure. The Simultaneous Multi-Slice (SMS) technique provides a reconstruction method where multiple slices are acquired and aliased concurrently. Traditional imaging techniques such as SENSE and GRAPPA can reconstruct an image from less measured data but have their drawbacks. The Controlled Aliasing in Parallel Imaging (CAIPI) and view angle tilting (VAT) techniques achieve slice-wise image shift to decrease the influence of the geometry factor (g-factor) of coil sensitivities and prevent the singular problem of the design matrix. In this paper, a Bayesian CAIPIVAT approach for multi-coil separation of parallel encoded complex-valued slices (mSPECS-CAIPIVAT) with a novel SMS approach is presented and combined with the Hadamard phase-encoding method for image separation. Our proposed approach was applied to simulation and experimental studies showing a decrease in the influence of the g-factor while increasing the brain activation detection rate. The signal-to-noise ratio and the contrast-to-noise ratio are also improved by our approach.

In fMRI, capturing brain activity during a task is dependent on how quickly the k-space arrays for each volume image are obtained. Acquiring the full k-space arrays can take a considerable amount of time. Under-sampling k-space reduces the acquisition time, but results in aliased, or “folded,” images after applying the inverse Fourier transform (IFT). GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) and SENSitivity Encoding (SENSE) are parallel imaging techniques that yield reconstructed images from subsampled arrays of k-space. With GRAPPA operating in the spatial frequency domain and SENSE in image space, these techniques have been separate but can be merged to reconstruct the subsampled k-space arrays more accurately. Here, we propose a Bayesian approach to this merged model where prior distributions for the unknown parameters are assessed from a priori k-space arrays. The prior information is utilized to estimate the missing spatial frequency values, unalias the voxel values from the posterior distribution, and reconstruct into full field-of-view images. Our Bayesian technique successfully reconstructed simulated and experimental fMRI time series with no aliasing artifacts while decreasing temporal variation and increasing task detection power.

In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic resonance imaging (fMRI) image reconstruction. The complex-valued linear model and our Bayesian model are evaluated through extensive simulations and applied to experimental fMRI data.

Functional magnetic resonance imaging (fMRI) plays a crucial role in neuroimaging, enabling the exploration of brain activity through complex-valued signals. These signals, composed of magnitude and phase, offer a rich source of information for understanding brain functions. Traditional fMRI analyses have largely focused on magnitude information, often overlooking the potential insights offered by phase data. In this paper, we propose a novel fully Bayesian model designed for analyzing single-subject complex-valued fMRI (cv-fMRI) data. Our model, which we refer to as the CV-M&P model, is distinctive in its comprehensive utilization of both magnitude and phase information in fMRI signals, allowing for independent prediction of different types of activation maps. We incorporate Gaussian Markov random fields (GMRFs) to capture spatial correlations within the data, and employ image partitioning and parallel computation to enhance computational efficiency. Our model is rigorously tested through simulation studies, and then applied to a real dataset from a unilateral finger-tapping experiment. The results demonstrate the model's effectiveness in accurately identifying brain regions activated in response to specific tasks, distinguishing between magnitude and phase activation.

Neural network pruning is a highly effective technique aimed at reducing the computational and memory demands of large neural networks. In this research paper, we present a novel approach to pruning neural networks utilizing Bayesian inference, which can seamlessly integrate into the training procedure. Our proposed method leverages the posterior probabilities of the neural network prior to and following pruning, enabling the calculation of Bayes factors. The calculated Bayes factors guide the iterative pruning. Through comprehensive evaluations conducted on multiple benchmarks, we demonstrate that our method achieves desired levels of sparsity while maintaining competitive accuracy.

We propose a model-based approach that combines Bayesian variable selection tools, a novel spatial kernel convolution structure, and autoregressive processes for detecting a subject's brain activation at the voxel level in complex-valued functional magnetic resonance imaging (CV-fMRI) data. A computationally efficient Markov chain Monte Carlo algorithm for posterior inference is developed by taking advantage of the dimension reduction of the kernel-based structure. The proposed spatiotemporal model leads to more accurate posterior probability activation maps and less false positives than alternative spatial approaches based on Gaussian process models, and other complex-valued models that do not incorporate spatial and/or temporal structure. This is illustrated in the analysis of simulated data and human task-related CV-fMRI data. In addition, we show that complex-valued approaches dominate magnitude-only approaches and that the kernel structure in our proposed model considerably improves sensitivity rates when detecting activation at the voxel level.

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method typical for nonlinear inverse problems, interpolation and embeddings are needed. To overcome this, we present a flexible framework to extend model-based learning directly to nonuniform meshes, by interpreting the mesh as a graph and formulating our network architectures using graph convolutional neural networks. This gives rise to the proposed iterative Graph Convolutional Newton-type Method (GCNM), which includes the forward model in the solution of the inverse problem, while all updates are directly computed by the network on the problem specific mesh. We present results for Electrical Impedance Tomography, a severely ill-posed nonlinear inverse problem that is frequently solved via optimization-based methods, where the forward problem is solved by finite element methods. Results for absolute EIT imaging are compared to standard iterative methods as well as a graph residual network. We show that the GCNM has good generalizability to different domain shapes and meshes, out of distribution data as well as experimental data, from purely simulated training data and without transfer training.

Voxel functional magnetic resonance imaging (fMRI) time courses are complex-valued signals giving rise to magnitude and phase data. Nevertheless, most studies use only the magnitude signals and thus discard half of the data that could potentially contain important information. Methods that make use of complex-valued fMRI (CV-fMRI) data have been shown to lead to superior power in detecting active voxels when compared to magnitude-only methods, particularly for small signal-to-noise ratios (SNRs). We present a new Bayesian variable selection approach for detecting brain activation at the voxel level from CV-fMRI data. We develop models with complex-valued spike-and-slab priors on the activation parameters that are able to combine the magnitude and phase information. We present a complex-valued EM variable selection algorithm that leads to fast detection at the voxel level in CV-fMRI slices and also consider full posterior inference via Markov chain Monte Carlo (MCMC). Model performance is illustrated through extensive simulation studies, including the analysis of physically based simulated CV-fMRI slices. Finally, we use the complex-valued Bayesian approach to detect active voxels in human CV-fMRI from a healthy individual who performed unilateral finger tapping in a designed experiment. The proposed approach leads to improved detection of activation in the expected motor-related brain regions and produces fewer false positive results than other methods for CV-fMRI. Supplementary materials for this article are available online.

A complex-valued data-based model with pth order autoregressive errors and general real/imaginary error covariance structure is proposed as an alternative to the commonly-used magnitude-only data-based autoregressive model for fMRI time series. Likelihood-ratio-test-based activation statistics are derived for both models and compared for experimental and simulated data. For a dataset from a right-hand finger-tapping experiment, the activation map obtained using complex-valued modeling more clearly identifies the primary activation region (left functional central sulcus) than the magnitude-only model. Such improved accuracy in mapping the left functional central sulcus has important implications in neurosurgical planning for tumor and epilepsy patients. Additionally, we develop magnitude and phase detrending procedures for complex-valued time series and examine the effect of spatial smoothing. These methods improve the power of complex-valued data-based activation statistics. Our results advocate for the use of the complex-valued data and the modeling of its dependence structures as a more efficient and reliable tool in fMRI experiments over the current practice of using only magnitude-valued datasets.

Simultaneous multislice (SMS) imaging can be used to decrease the time between acquisition of fMRI volumes, which can increase sensitivity by facilitating the removal of higher-frequency artifacts and boosting effective sample size. The technique requires an additional processing step in which the slices are separated, or unaliased, to recover the whole brain volume. However, this may result in signal "leakage" between aliased locations, i.e., slice "leakage," and lead to spurious activation (decreased specificity). SMS can also lead to noise amplification, which can reduce the benefits of decreased repetition time. In this study, we evaluate the original slice-GRAPPA (no leak block) reconstruction algorithm and acceleration factor (AF = 8) used in the fMRI data in the young adult Human Connectome Project (HCP). We also evaluate split slice-GRAPPA (leak block), which can reduce slice leakage. We use simulations to disentangle higher test statistics into true positives (sensitivity) and false positives (decreased specificity). Slice leakage was greatly decreased by split slice-GRAPPA. Noise amplification was decreased by using moderate acceleration factors (AF = 4). We examined slice leakage in unprocessed fMRI motor task data from the HCP. When data were smoothed, we found evidence of slice leakage in some, but not all, subjects. We also found evidence of SMS noise amplification in unprocessed task and processed resting-state HCP data.

Increasing temporal resolution while mitigating signal leakage has been a challenge of simultaneous multi-slice (SMS) imaging in functional magnetic resonance imaging. The MultiCoil Separation of Parallel Encoded Complex-valued Slices (mSPECS) reconstruction method minimizes residual signal artifacts from time-series un-aliasing, and preserves the blood oxygen level dependent (BOLD) signal in fMRI studies. In the mSPECS reconstruction model, multiple slices are simultaneously excited with a Hadamard multiband pulse sequence. With Hadamard encoded acquisitions, the separated images have increased sensitivity with no net reduction in the scan duration. The mSPECS reconstruction method has incorporated the spatial information from a phased array of receiver coils, combined with a bootstrap sampling and artificial Hadamard aliasing of calibration images, to separate the fMRI time-series with a visual task in a least squares estimation. Faster brain function observation is dynamically achieved post data acquisition in a visual task fMRI experiment. The aliased slices are effectively separated, and functional activation is detected in the visual cortex. The mSPECS model has combined calibration images with intrinsic orthogonal properties of Hadamard encoding, into a un-aliasing estimator to achieve separated images of fMRI time-series.

PurposeAchieving a reduction in scan time with minimal inter-slice signal leakage is one of the significant obstacles in parallel MR imaging. In fMRI, multiband-imaging techniques accelerate data acquisition by simultaneously magnetizing the spatial frequency spectrum of multiple slices. The SPECS model eliminates the consequential inter-slice signal leakage from the slice unaliasing, while maintaining an optimal reduction in scan time and activation statistics in fMRI studies.Materials and methodsWhen the combined k-space array is inverse Fourier reconstructed, the resulting aliased image is separated into the un-aliased slices through a least squares estimator. Without the additional spatial information from a phased array of receiver coils, slice separation in SPECS is accomplished with acquired aliased images in shifted FOV aliasing pattern, and a bootstrapping approach of incorporating reference calibration images in an orthogonal Hadamard pattern.ResultThe aliased slices are effectively separated with minimal expense to the spatial and temporal resolution. Functional activation is observed in the motor cortex, as the number of aliased slices is increased, in a bilateral finger tapping fMRI experiment.ConclusionThe SPECS model incorporates calibration reference images together with coefficients of orthogonal polynomials into an un-aliasing estimator to achieve separated images, with virtually no residual artifacts and functional activation detection in separated images.

PURPOSE:To develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis.MATERIALS AND METHODS:The standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform of MO and CV correlations for varying degrees of task related magnitude and phase amplitude change in the time-series. The increased sensitivity of the complex-valued Fourier representation of correlation is also demonstrated with experimental human data. Since the correlation description in the temporal frequency domain is represented as a summation of second order temporal frequencies, the correlation is easily divided into experimentally relevant frequency bands for each voxel's temporal frequency spectrum. The MO and CV correlations for the experimental human data are analyzed for four voxels of interest (VOIs) to show the framework with high and low contrast-to-noise ratios in the motor cortex and the supplementary motor cortex.RESULTS:The simulation demonstrates the increased strength of CV correlations over MO correlations for low magnitude contrast-to-noise time-series. In the experimental human data, the MO correlation maps are noisier than the CV maps, and it is more difficult to distinguish the motor cortex in the MO correlation maps after spatial processing.CONCLUSIONS:Including both magnitude and phase in the spatial correlation computations more accurately defines the correlated left and right motor cortices. Sensitivity in correlation analysis is important to preserve the signal of interest in fMRI data sets with high noise variance, and avoid excessive processing induced correlation.

PurposeTo develop a mathematical model that incorporates the magnetic resonance relaxivities into the image reconstruction process in a single step.Materials and methodsIn magnetic resonance imaging, the complex-valued measurements of the acquired signal at each point in frequency space are expressed as a Fourier transformation of the proton spin density weighted by Fourier encoding anomalies: T2⁎, T1, and a phase determined by magnetic field inhomogeneity (∆B) according to the MR signal equation. Such anomalies alter the expected symmetry and the signal strength of the k-space observations, resulting in images distorted by image warping, blurring, and loss in image intensity. Although T1 on tissue relaxation time provides valuable quantitative information on tissue characteristics, the T1 recovery term is typically neglected by assuming a long repetition time. In this study, the linear framework presented in the work of Rowe et al., 2007, and of Nencka et al., 2009 is extended to develop a Fourier reconstruction operation in terms of a real-valued isomorphism that incorporates the effects of T2⁎, ∆B, and T1. This framework provides a way to precisely quantify the statistical properties of the corrected image-space data by offering a linear relationship between the observed frequency space measurements and reconstructed corrected image-space measurements. The model is illustrated both on theoretical data generated by considering T2⁎, T1, and/or ∆B effects, and on experimentally acquired fMRI data by focusing on the incorporation of T1. A comparison is also made between the activation statistics computed from the reconstructed data with and without the incorporation of T1 effects.ResultAccounting for T1 effects in image reconstruction is shown to recover image contrast that exists prior to T1 equilibrium. The incorporation of T1 is also shown to induce negligible correlation in reconstructed images and preserve functional activations.ConclusionWith the use of the proposed method, the effects of T2⁎ and ∆B can be corrected, and T1 can be incorporated into the time series image-space data during image reconstruction in a single step. Incorporation of T1 provides improved tissue segmentation over the course of time series and therefore can improve the precision of motion correction and image registration.