Search

Large annotated datasets are required for training deep learning models, but in medical imaging data sharing is often complicated due to ethics, anonymization and data protection legislation. Generative AI models, such as generative adversarial networks (GANs) and diffusion models, can today produce very realistic synthetic images, and can potentially facilitate data sharing. However, in order to share synthetic medical images it must first be demonstrated that they can be used for training different networks with acceptable performance. Here, we therefore comprehensively evaluate four GANs (progressive GAN, StyleGAN 1-3) and a diffusion model for the task of brain tumor segmentation (using two segmentation networks, U-Net and a Swin transformer). Our results show that segmentation networks trained on synthetic images reach Dice scores that are 80% - 90% of Dice scores when training with real images, but that memorization of the training images can be a problem for diffusion models if the original dataset is too small. Our conclusion is that sharing synthetic medical images is a viable option to sharing real images, but that further work is required. The trained generative models and the generated synthetic images are shared on AIDA data hub, Comment: 28 Pages. 5 figures

Diffusion models were initially developed for text-to-image generation and are now being utilized to generate high quality synthetic images. Preceded by GANs, diffusion models have shown impressive results using various evaluation metrics. However, commonly used metrics such as FID and IS are not suitable for determining whether diffusion models are simply reproducing the training images. Here we train StyleGAN and a diffusion model, using BRATS20, BRATS21 and a chest x-ray pneumonia dataset, to synthesize brain MRI and chest x-ray images, and measure the correlation between the synthetic images and all training images. Our results show that diffusion models are more likely to memorize the training images, compared to StyleGAN, especially for small datasets and when using 2D slices from 3D volumes. Researchers should be careful when using diffusion models (and to some extent GANs) for medical imaging, if the final goal is to share the synthetic images., Comment: 14 Pages, 6 Figures

Using 3D CNNs on high resolution medical volumes is very computationally demanding, especially for large datasets like the UK Biobank which aims to scan 100,000 subjects. Here we demonstrate that using 2D CNNs on a few 2D projections (representing mean and standard deviation across axial, sagittal and coronal slices) of the 3D volumes leads to reasonable test accuracy when predicting the age from brain volumes. Using our approach, one training epoch with 20,324 subjects takes 20 - 50 seconds using a single GPU, which two orders of magnitude faster compared to a small 3D CNN. These results are important for researchers who do not have access to expensive GPU hardware for 3D CNNs.

Large annotated datasets are required to train segmentation networks. In medical imaging, it is often difficult, time consuming and expensive to create such datasets, and it may also be difficult to share these datasets with other researchers. Different AI models can today generate very realistic synthetic images, which can potentially be openly shared as they do not belong to specific persons. However, recent work has shown that using synthetic images for training deep networks often leads to worse performance compared to using real images. Here we demonstrate that using synthetic images and annotations from an ensemble of 20 GANs, instead of from a single GAN, increases the Dice score on real test images with 4.7 % to 14.0 % on specific classes., Comment: 5 pages, submitted to ISBI 2023

Diffusion MRI (dMRI) is the only non-invasive technique sensitive to tissue micro-architecture, which can, in turn, be used to reconstruct tissue microstructure and white matter pathways. The accuracy of such tasks is hampered by the low signal-to-noise ratio in dMRI. Today, the noise is characterized mainly by visual inspection of residual maps and estimated standard deviation. However, it is hard to estimate the impact of noise on downstream tasks based only on such qualitative assessments. To address this issue, we introduce a novel metric, Noise Uncertainty Quantification (NUQ), for quantitative image quality analysis in the absence of a ground truth reference image. NUQ uses a recent Bayesian formulation of dMRI models to estimate the uncertainty of microstructural measures. Specifically, NUQ uses the maximum mean discrepancy metric to compute a pooled quality score by comparing samples drawn from the posterior distribution of the microstructure measures. We show that NUQ allows a fine-grained analysis of noise, capturing details that are visually imperceptible. We perform qualitative and quantitative comparisons on real datasets, showing that NUQ generates consistent scores across different denoisers and acquisitions. Lastly, by using NUQ on a cohort of schizophrenics and controls, we quantify the substantial impact of denoising on group differences.

In the application of deep learning on optical coherence tomography (OCT) data, it is common to train classification networks using 2D images originating from volumetric data. Given the micrometer resolution of OCT systems, consecutive images are often very similar in both visible structures and noise. Thus, an inappropriate data split can result in overlap between the training and testing sets, with a large portion of the literature overlooking this aspect. In this study, the effect of improper dataset splitting on model evaluation is demonstrated for three classification tasks using three OCT open-access datasets extensively used, Kermany's and Srinivasan's ophthalmology datasets, and AIIMS breast tissue dataset. Results show that the classification performance is inflated by 0.07 up to 0.43 in terms of Matthews Correlation Coefficient (accuracy: 5% to 30%) for models tested on datasets with improper splitting, highlighting the considerable effect of dataset handling on model evaluation. This study intends to raise awareness on the importance of dataset splitting given the increased research interest in implementing deep learning on OCT data., Comment: 8 pages, 2 figures

Analysis of brain connectivity is important for understanding how information is processed by the brain. We propose a novel Bayesian vector autoregression (VAR) hierarchical model for analyzing brain connectivity in a resting-state fMRI data set with autism spectrum disorder (ASD) patients and healthy controls. Our approach models functional and effective connectivity simultaneously, which is new in the VAR literature for brain connectivity, and allows for both group- and single-subject inference as well as group comparisons. We combine analytical marginalization with Hamiltonian Monte Carlo (HMC) to obtain highly efficient posterior sampling. The results from more simplified covariance settings are, in general, overly optimistic about functional connectivity between regions compared to our results. In addition, our modeling of heterogeneous subject-specific covariance matrices is shown to give smaller differences in effective connectivity compared to models with a common covariance matrix to all subjects., Comment: 21 pages, 5 figures

Classifying subjects as healthy or diseased using neuroimaging data has gained a lot of attention during the last 10 years. Here we apply deep learning to derivatives from resting state fMRI data, and investigate how different 3D augmentation techniques affect the test accuracy. Specifically, we use resting state derivatives from 1,112 subjects in ABIDE preprocessed to train a 3D convolutional neural network (CNN) to perform the classification. Our results show that augmentation only provide minor improvements to the test accuracy.

Training segmentation networks requires large annotated datasets, which in medical imaging can be hard to obtain. Despite this fact, data augmentation has in our opinion not been fully explored for brain tumor segmentation. In this project we apply different types of data augmentation (flipping, rotation, scaling, brightness adjustment, elastic deformation) when training a standard 3D U-Net, and demonstrate that augmentation significantly improves the network's performance in many cases. Our conclusion is that brightness augmentation and elastic deformation work best, and that combinations of different augmentation techniques do not provide further improvement compared to only using one augmentation technique. Our code is available at https://github.com/mdciri/3D-augmentation-techniques.

Effective, robust, and automatic tools for brain tumor segmentation are needed for the extraction of information useful in treatment planning from magnetic resonance (MR) images. Context-aware artificial intelligence is an emerging concept for the development of deep learning applications for computer-aided medical image analysis. In this work, it is investigated whether the addition of contextual information from the brain anatomy in the form of white matter, gray matter, and cerebrospinal fluid masks and probability maps improves U-Net-based brain tumor segmentation. The BraTS2020 dataset was used to train and test two standard 3D U-Net models that, in addition to the conventional MR image modalities, used the anatomical contextual information as extra channels in the form of binary masks (CIM) or probability maps (CIP). A baseline model (BLM) that only used the conventional MR image modalities was also trained. The impact of adding contextual information was investigated in terms of overall segmentation accuracy, model training time, domain generalization, and compensation for fewer MR modalities available for each subject. Results show that there is no statistically significant difference when comparing Dice scores between the baseline model and the contextual information models, even when comparing performances for high- and low-grade tumors independently. Only in the case of compensation for fewer MR modalities available for each subject did the addition of anatomical contextual information significantly improve the segmentation of the whole tumor. Overall, there is no overall significant improvement in segmentation performance when using anatomical contextual information in the form of either binary masks or probability maps as extra channels.

Training segmentation networks requires large annotated datasets, but manual annotation is time consuming and costly. We here investigate if the combination of a noise-to-image GAN and an image-to-image GAN can be used to synthesize realistic brain tumor images as well as the corresponding tumor annotations (labels), to substantially increase the number of training images. The noise-to-image GAN is used to synthesize new label images, while the image-to-image GAN generates the corresponding MR image from the label image. Our results indicate that the two GANs can synthesize label images and MR images that look realistic, and that adding synthetic images improves the segmentation performance, although the effect is small.

We investigate the origin of the experimentally observed varying current-frequency nonlinearity of the propagating spin wave mode in nano-contact spin torque oscillators. Nominally identical devices with 100 nm diameter are characterized by electrical microwave measurements and show large variation in the generated frequency as a function of drive current. This quantitative and qualitative device-to-device variation is described in terms of continuous and discontinuous nonlinear transitions between linear current intervals. The thin film grain microstructure in our samples is determined using atomic force and scanning electron microscopy to be on the scale of 30 nm. Micromagnetic simulations show that the reflection of spin waves against the grain boundaries results in standing wave resonance configurations. For a simulated device with a single artificial grain, the frequency increases linearly with the drive current until the decreased wavelength eventually forces another spin wave anti-node to be formed. This transition results in a discontinuous step in the frequency versus current relation. Simulations of complete, randomly generated grain microstructures additionally shows continuous nonlinearity and a resulting device-to-device variation in frequency that is similar to the experimental levels. The impact of temperature from 4 K to 300 K on the resonance mode-transition nonlinearity and frequency noise is investigated using simulations and it is found that the peak levels of the spectral linewidth as a function of drive current agrees quantitatively with typical levels found in experiments at room temperature.

Gliomas are the most common primary brain malignancies, with different degrees of aggressiveness, variable prognosis and various heterogeneous histological sub-regions, i.e., peritumoral edema, necrotic core, enhancing and non-enhancing tumour core. Although brain tumours can easily be detected using multi-modal MRI, accurate tumor segmentation is a challenging task. Hence, using the data provided by the BraTS Challenge 2020, we propose a 3D volume-to-volume Generative Adversarial Network for segmentation of brain tumours. The model, called Vox2Vox, generates realistic segmentation outputs from multi-channel 3D MR images, segmenting the whole, core and enhancing tumor with mean values of 87.20%, 81.14%, and 78.67% as dice scores and 6.44mm, 24.36mm, and 18.95mm for Hausdorff distance 95 percentile for the BraTS testing set after ensembling 10 Vox2Vox models obtained with a 10-fold cross-validation.

Deep learning requires large datasets for training (convolutional) networks with millions of parameters. In neuroimaging, there are few open datasets with more than 100 subjects, which makes it difficult to, for example, train a classifier to discriminate controls from diseased persons. Generative adversarial networks (GANs) can be used to synthesize data, but virtually all research is focused on 2D images. In medical imaging, and especially in neuroimaging, most datasets are 3D or 4D. Here we therefore present preliminary results showing that a 3D progressive growing GAN can be used to synthesize MR brain volumes.

Brain activation mapping using functional MRI (fMRI) based on blood oxygenation level-dependent (BOLD) contrast has been conventionally focused on probing gray matter, the BOLD contrast in white matter having been generally disregarded. Recent results have provided evidence of the functional significance of the white matter BOLD signal, showing at the same time that its correlation structure is highly anisotropic, and related to the diffusion tensor in shape and orientation. This evidence suggests that conventional isotropic Gaussian filters are inadequate for denoising white matter fMRI data, since they are incapable of adapting to the complex anisotropic domain of white matter axonal connections. In this paper we explore a graph-based description of the white matter developed from diffusion MRI data, which is capable of encoding the anisotropy of the domain. Based on this representation we design localized spatial filters that adapt to white matter structure by leveraging graph signal processing principles. The performance of the proposed filtering technique is evaluated on semi-synthetic data, where it shows potential for greater sensitivity and specificity in white matter activation mapping, compared to isotropic filtering.

Existing Bayesian spatial priors for functional magnetic resonance imaging (fMRI) data correspond to stationary isotropic smoothing filters that may oversmooth at anatomical boundaries. We propose two anatomically informed Bayesian spatial models for fMRI data with local smoothing in each voxel based on a tensor field estimated from a T1-weighted anatomical image. We show that our anatomically informed Bayesian spatial models results in posterior probability maps that follow the anatomical structure.

The time domain stability of microwave spin torque oscillators (STOs) has been investigated by systematic micromagnetic simulations. A model based on internal spin wave reflection at grain boundaries with reduced exchange coupling was implemented and used to study the oscillator under quasi-stable operating conditions. Telegraphic mode jumping between two operating frequencies (23.3 and 24.1 GHz) was observed in the time domain with characteristic dwell times in the range of 10-100 ns. The oscillating volume was shown to have a different shape at the distinct operating frequencies. The shape difference is governed by spin wave reflections at the grain boundaries. The resulting non-linear behavior of the oscillator was shown to be a collective effect of spin wave scattering at different locations within a few spin wavelengths from the nano-contact., Comment: Presented at the 25th International Conference on Noise and Fluctuations ICNF 2019, Neuchatel, Switzerland, June 18-21, 2019

Registration between an fMRI volume and a T1-weighted volume is challenging, since fMRI volumes contain geometric distortions. Here we present preliminary results showing that 3D CycleGAN can be used to synthesize fMRI volumes from T1-weighted volumes, and vice versa, which can facilitate registration.

Bayesian whole-brain functional magnetic resonance imaging (fMRI) analysis with three-dimensional spatial smoothing priors has been shown to produce state-of-the-art activity maps without pre-smoothing the data. The proposed inference algorithms are computationally demanding however, and the proposed spatial priors have several less appealing properties, such as being improper and having infinite spatial range. We propose a statistical inference framework for whole-brain fMRI analysis based on the class of Mat\'ern covariance functions. The framework uses the Gaussian Markov random field (GMRF) representation of possibly anisotropic spatial Mat\'ern fields via the stochastic partial differential equation (SPDE) approach of Lindgren et al. (2011). This allows for more flexible and interpretable spatial priors, while maintaining the sparsity required for fast inference in the high-dimensional whole-brain setting. We develop an accelerated stochastic gradient descent (SGD) optimization algorithm for empirical Bayes (EB) inference of the spatial hyperparameters. Conditionally on the inferred hyperparameters, we make a fully Bayesian treatment of the brain activity. The Mat\'ern prior is applied to both simulated and experimental task-fMRI data and clearly demonstrates that it is a more reasonable choice than the previously used priors, using comparisons of activity maps, prior simulation and cross-validation.

The human brain cortical layer has a convoluted morphology that is unique to each individual. Characterization of the cortical morphology is necessary in longitudinal studies of structural brain change, as well as in discriminating individuals in health and disease. A method for encoding the cortical morphology in the form of a graph is presented. The design of graphs that encode the global cerebral hemisphere cortices as well as localized cortical regions is proposed. Spectral metrics derived from these graphs are then studied and proposed as descriptors of cortical morphology. As proof-of-concept of their applicability in characterizing cortical morphology, the metrics are studied in the context of hemispheric asymmetry as well as gender dependent discrimination of cortical morphology., Comment: arXiv admin note: substantial text overlap with arXiv:1810.10339

The human brain cortical layer has a convoluted morphology that is unique to each individual. Characterization of the cortical morphology is necessary in longitudinal studies of structural brain change, as well as in discriminating individuals in health and disease. A method for encoding the cortical morphology in the form of a graph is presented. The design of graphs that encode the global cerebral hemisphere cortices as well as localized cortical regions is proposed. Spectral features of these graphs are then studied and proposed as descriptors of cortical morphology. As proof-of-concept of their applicability in characterizing cortical morphology, the descriptors are studied in the context of discriminating individuals based on their sex.

Anonymization of medical images is necessary for protecting the identity of the test subjects, and is therefore an essential step in data sharing. However, recent developments in deep learning may raise the bar on the amount of distortion that needs to be applied to guarantee anonymity. To test such possibilities, we have applied the novel CycleGAN unsupervised image-to-image translation framework on sagittal slices of T1 MR images, in order to reconstruct facial features from anonymized data. We applied the CycleGAN framework on both face-blurred and face-removed images. Our results show that face blurring may not provide adequate protection against malicious attempts at identifying the subjects, while face removal provides more robust anonymization, but is still partially reversible.

One-sided t-tests are commonly used in the neuroimaging field, but two-sided tests should be the default unless a researcher has a strong reason for using a one-sided test. Here we extend our previous work on cluster false positive rates, which used one-sided tests, to two-sided tests. Briefly, we found that parametric methods perform worse for two-sided t-tests, and that non-parametric methods perform equally well for one-sided and two-sided tests.

Diffusion magnetic resonance imaging (diffusion MRI) is a non-invasive microstructure assessment technique. Scalar measures, such as FA (fractional anisotropy) and MD (mean diffusivity), quantifying micro-structural tissue properties can be obtained using diffusion models and data processing pipelines. However, it is costly and time consuming to collect high quality diffusion data. Here, we therefore demonstrate how Generative Adversarial Networks (GANs) can be used to generate synthetic diffusion scalar measures from structural T1-weighted images in a single optimized step. Specifically, we train the popular CycleGAN model to learn to map a T1 image to FA or MD, and vice versa. As an application, we show that synthetic FA images can be used as a target for non-linear registration, to correct for geometric distortions common in diffusion MRI.

In medical imaging, a general problem is that it is costly and time consuming to collect high quality data from healthy and diseased subjects. Generative adversarial networks (GANs) is a deep learning method that has been developed for synthesizing data. GANs can thereby be used to generate more realistic training data, to improve classification performance of machine learning algorithms. Another application of GANs is image-to-image translations, e.g. generating magnetic resonance (MR) images from computed tomography (CT) images, which can be used to obtain multimodal datasets from a single modality. Here, we evaluate two unsupervised GAN models (CycleGAN and UNIT) for image-to-image translation of T1- and T2-weighted MR images, by comparing generated synthetic MR images to ground truth images. We also evaluate two supervised models; a modification of CycleGAN and a pure generator model. A small perceptual study was also performed to evaluate how visually realistic the synthesized images are. It is shown that the implemented GAN models can synthesize visually realistic MR images (incorrectly labeled as real by a human). It is also shown that models producing more visually realistic synthetic images not necessarily have better quantitative error measurements, when compared to ground truth data. Code is available at https://github.com/simontomaskarlsson/GAN-MRI

Methodological research rarely generates a broad interest, yet our work on the validity of cluster inference methods for functional magnetic resonance imaging (fMRI) created intense discussion on both the minutia of our approach and its implications for the discipline. In the present work, we take on various critiques of our work and further explore the limitations of our original work. We address issues about the particular event-related designs we used, considering multiple event types and randomisation of events between subjects. We consider the lack of validity found with one-sample permutation (sign flipping) tests, investigating a number of approaches to improve the false positive control of this widely used procedure. We found that the combination of a two-sided test and cleaning the data using ICA FIX resulted in nominal false positive rates for all datasets, meaning that data cleaning is not only important for resting state fMRI, but also for task fMRI. Finally, we discuss the implications of our work on the fMRI literature as a whole, estimating that at least 10% of the fMRI studies have used the most problematic cluster inference method (P = 0.01 cluster defining threshold), and how individual studies can be interpreted in light of our findings. These additional results underscore our original conclusions, on the importance of data sharing and thorough evaluation of statistical methods on realistic null data.

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification., Comment: Added results from a group analysis and a comparison with residual bootstrap

Background: Inference from fMRI data faces the challenge that the hemodynamic system that relates neural activity to the observed BOLD fMRI signal is unknown. New Method: We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modeled nonparametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD response, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in a flexible way, and simultaneously gives us the nonparametric flexibility of the GP. Results: Results on simulated data show that the proposed model is able to discriminate between active and non-active voxels also when the GP prior deviates from the true hemodynamics. Our model finds time varying dynamics when applied to real fMRI data. Comparison with Existing Method(s): The proposed model is better at detecting activity in simulated data than standard models, without inflating the false positive rate. When applied to real fMRI data, our GP model in several cases finds brain activity where previously proposed LTI models does not. Conclusions: We have proposed a new non-linear model for the hemodynamics in task fMRI, that is able to detect active voxels, and gives the opportunity to ask new kinds of questions related to hemodynamics., Comment: 18 pages, 14 figures

We are glad that our paper has generated intense discussions in the fMRI field, on how to analyze fMRI data and how to correct for multiple comparisons. The goal of the paper was not to disparage any specific fMRI software, but to point out that parametric statistical methods are based on a number of assumptions that are not always valid for fMRI data, and that non-parametric statistical methods are a good alternative. Through AFNIs introduction of non-parametric statistics in the function 3dttest++, the three most common fMRI softwares now all support non-parametric group inference (SPM through the toolbox SnPM, and FSL through the function randomise).

A recent Editorial by Slotnick (2017) reconsiders the findings of our paper on the accuracy of false positive rate control with cluster inference in fMRI (Eklund et al, 2016), in particular criticising our use of resting state fMRI data as a source for null data in the evaluation of task fMRI methods. We defend this use of resting fMRI data, as while there is much structure in this data, we argue it is representative of task data noise and as such analysis software should be able to accommodate this noise. We also discuss a potential problem with Slotnick's own method., Comment: Update: Title changed to be more informative, abstract expanded. Body text unchanged

We propose a regression model for non-central $\chi$ (NC-$\chi$) distributed functional magnetic resonance imaging (fMRI) and diffusion weighted imaging (DWI) data, with the heteroscedastic Rician regression model as a prominent special case. The model allows both parameters in the NC-$\chi$ distribution to be linked to explanatory variables, with the relevant covariates automatically chosen by Bayesian variable selection. A highly efficient Markov chain Monte Carlo (MCMC) algorithm is proposed for simulating from the joint Bayesian posterior distribution of all model parameters and the binary covariate selection indicators. Simulated fMRI data is used to demonstrate that the Rician model is able to localize brain activity much more accurately than the traditionally used Gaussian model at low signal-to-noise ratios. Using a diffusion dataset from the Human Connectome Project, it is also shown that the commonly used approximate Gaussian noise model underestimates the mean diffusivity (MD) and the fractional anisotropy (FA) in the single-diffusion tensor model compared to the theoretically correct Rician model.

We propose a voxel-wise general linear model with autoregressive noise and heteroscedastic noise innovations (GLMH) for analyzing functional magnetic resonance imaging (fMRI) data. The model is analyzed from a Bayesian perspective and has the benefit of automatically down-weighting time points close to motion spikes in a data-driven manner. We develop a highly efficient Markov Chain Monte Carlo (MCMC) algorithm that allows for Bayesian variable selection among the regressors to model both the mean (i.e., the design matrix) and variance. This makes it possible to include a broad range of explanatory variables in both the mean and variance (e.g., time trends, activation stimuli, head motion parameters and their temporal derivatives), and to compute the posterior probability of inclusion from the MCMC output. Variable selection is also applied to the lags in the autoregressive noise process, making it possible to infer the lag order from the data simultaneously with all other model parameters. We use both simulated data and real fMRI data from OpenfMRI to illustrate the importance of proper modeling of heteroscedasticity in fMRI data analysis. Our results show that the GLMH tends to detect more brain activity, compared to its homoscedastic counterpart, by allowing the variance to change over time depending on the degree of head motion.

We propose to use Gaussian process regression to accurately estimate the diffusion MRI signal at arbitrary locations in q-space. By estimating the signal on a grid, we can do synthetic diffusion spectrum imaging: reconstructing the ensemble averaged propagator (EAP) by an inverse Fourier transform. We also propose an alternative reconstruction method guaranteeing a nonnegative EAP that integrates to unity. The reconstruction is validated on data simulated from two Gaussians at various crossing angles. Moreover, we demonstrate on non-uniformly sampled in vivo data that the method is far superior to linear interpolation, and allows a drastic undersampling of the data with only a minor loss of accuracy. We envision the method as a potential replacement for standard diffusion spectrum imaging, in particular when acquistion time is limited., Comment: 5 pages

Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a great computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do approximate inference without comparison to the true posterior distribution. A popular such method, which is now the standard method for Bayesian single subject analysis in the SPM software, is introduced in Penny et al. (2005b). The method processes the data slice-by-slice and uses an approximate variational Bayes (VB) estimation algorithm that enforces posterior independence between activity coefficients in different voxels. We introduce a fast and practical Markov chain Monte Carlo (MCMC) scheme for exact inference in the same model, both slice-wise and for the whole brain using a 3D prior on activity coefficients. The algorithm exploits sparsity and uses modern techniques for efficient sampling from high-dimensional Gaussian distributions, leading to speed-ups without which MCMC would not be a practical option. Using MCMC, we are for the first time able to evaluate the approximate VB posterior against the exact MCMC posterior, and show that VB can lead to spurious activation. In addition, we develop an improved VB method that drops the assumption of independent voxels a posteriori. This algorithm is shown to be much faster than both MCMC and the original VB for large datasets, with negligible error compared to the MCMC posterior.