Noise-reduction techniques for 1H-FID-MRSI at 14.1T: Monte-Carlo validation & in vivo application

Proton magnetic resonance spectroscopic imaging (1H-MRSI) is a powerful tool that enables the multidimensional non-invasive mapping of the neurochemical profile at high-resolution over the entire brain. The constant demand for higher spatial resolution in 1H-MRSI led to increased interest in post-processing-based denoising methods aimed at reducing noise variance. The aim of the present study was to implement two noise-reduction techniques, the Marchenko-Pastur principal component analysis (MP-PCA) based denoising and the low-rank total generalized variation (LR-TGV) reconstruction, and to test their potential and impact on preclinical 14.1T fast in vivo 1H-FID-MRSI datasets. Since there is no known ground truth for in vivo metabolite maps, additional evaluations of the performance of both noise-reduction strategies were conducted using Monte-Carlo simulations. Results showed that both denoising techniques increased the apparent signal-to-noise ratio SNR while preserving noise properties in each spectrum for both in vivo and Monte-Carlo datasets. Relative metabolite concentrations were not significantly altered by either methods and brain regional differences were preserved in both synthetic and in vivo datasets. Increased precision of metabolite estimates was observed for the two methods, with inconsistencies noted on lower concentrated metabolites. Our study provided a framework on how to evaluate the performance of MP-PCA and LR-TGV methods for preclinical 1H-FID MRSI data at 14.1T. While gains in apparent SNR and precision were observed, concentration estimations ought to be treated with care especially for low-concentrated metabolites.Comment: Brayan Alves and Dunja Simicic are joint first authors. Currently in revision for NMR in Biomedicin

Lagrangian Time Series Models for Ocean Surface Drifter Trajectories

This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer important physical parameters of inertial oscillations and other ocean processes. Nonstationary time series methods are employed to account for the spatiotemporal variability of each trajectory. Because the datasets are large, we construct computationally efficient methods through the use of frequency-domain modelling and estimation, with the data expressed as complex-valued time series. We detail how practical issues related to sampling and model misspecification may be addressed using semi-parametric techniques for time series, and we demonstrate the effectiveness of our stochastic models through application to both real-world data and to numerical model output.Comment: 21 pages, 10 figure

A subspace approach to high-resolution magnetic resonance spectroscopic imaging

With its unique capability to obtain spatially resolved biochemical profiles from the human body noninvasively, magnetic resonance spectroscopic imaging (MRSI) has been recognized as a powerful tool for in vivo metabolic studies. However, research and clinical applications of in vivo MRSI have been progressing more slowly than expected. The main reasons for this situation are the problems of long data acquisition time, poor spatial resolution and low signal-to-noise ratio (SNR) for this imaging modality. In the last four decades, significant efforts have been made to improve MRSI, resulting in a large number of fast pulse sequences and advanced image reconstruction methods. However, the existing techniques have yet to offer the levels of improvement in imaging time, spatial resolution and SNR necessary to significantly impact in vivo applications of MRSI. This thesis work develops a new subspace imaging approach to address these technical challenges to enable fast, high-resolution MRSI with high SNR. The proposed approach, coined SPICE (Spectroscopic Imaging by Exploiting Spatiospectral Correlation), is characterized by using a subspace model for integrative data acquisition, processing and image reconstruction. More specifically, SPICE represents the spectroscopic signals in MRSI using the partial separability (PS) model. The PS model implies that the high-dimensional spectroscopic signals reside in a low-dimensional subspace, which enables the design of special sparse sampling strategies for accelerated spatiospectral encoding and special image reconstruction strategies for determining the subspace and reconstructing the underlying spatiospectral function of interest from the sparse data. Using the SPICE framework, new data acquisition and image reconstruction methods are developed to enable high-resolution 1H-MRSI of the brain. We have evaluated SPICE using theoretical analysis, numerical simulations, phantom and in vivo experimental studies. Results obtained from these experiments demonstrate the unprecedented capability of SPICE in achieving accelerated MRSI with simultaneously very high resolution and SNR. We expect SPICE to provide a powerful tool for in vivo metabolic studies with many exciting applications. Furthermore, the SPICE framework also presents new opportunities for future developments in subspace-driven signal generation, signal encoding, data processing and image reconstruction methods to advance the research and clinical applications of high-resolution in vivo MRSI

Receptive Field Inference with Localized Priors

The linear receptive field describes a mapping from sensory stimuli to a one-dimensional variable governing a neuron's spike response. However, traditional receptive field estimators such as the spike-triggered average converge slowly and often require large amounts of data. Bayesian methods seek to overcome this problem by biasing estimates towards solutions that are more likely a priori, typically those with small, smooth, or sparse coefficients. Here we introduce a novel Bayesian receptive field estimator designed to incorporate locality, a powerful form of prior information about receptive field structure. The key to our approach is a hierarchical receptive field model that flexibly adapts to localized structure in both spacetime and spatiotemporal frequency, using an inference method known as empirical Bayes. We refer to our method as automatic locality determination (ALD), and show that it can accurately recover various types of smooth, sparse, and localized receptive fields. We apply ALD to neural data from retinal ganglion cells and V1 simple cells, and find it achieves error rates several times lower than standard estimators. Thus, estimates of comparable accuracy can be achieved with substantially less data. Finally, we introduce a computationally efficient Markov Chain Monte Carlo (MCMC) algorithm for fully Bayesian inference under the ALD prior, yielding accurate Bayesian confidence intervals for small or noisy datasets

A Spatiotemporal White Noise Analysis of Photoreceptor Responses to UV and Green Light in the Dragonfly Median Ocellus

Adult dragonflies augment their compound eyes with three simple eyes known as the dorsal ocelli. While the ocellar system is known to mediate stabilizing head reflexes during flight, the ability of the ocellar retina to dynamically resolve the environment is unknown. For the first time, we directly measured the angular sensitivities of the photoreceptors of the dragonfly median (middle) ocellus. We performed a second-order Wiener Kernel analysis of intracellular recordings of light-adapted photoreceptors. These were stimulated with one-dimensional horizontal or vertical patterns of concurrent UV and green light with different contrast levels and at different ambient temperatures. The photoreceptors were found to have anisotropic receptive fields with vertical and horizontal acceptance angles of 15° and 28°, respectively. The first-order (linear) temporal kernels contained significant undershoots whose amplitudes are invariant under changes in the contrast of the stimulus but significantly reduced at higher temperatures. The second-order kernels showed evidence of two distinct nonlinear components: a fast acting self-facilitation, which is dominant in the UV, followed by delayed self- and cross-inhibition of UV and green light responses. No facilitatory interactions between the UV and green light were found, indicating that facilitation of the green and UV responses occurs in isolated compartments. Inhibition between UV and green stimuli was present, indicating that inhibition occurs at a common point in the UV and green response pathways. We present a nonlinear cascade model (NLN) with initial stages consisting of separate UV and green pathways. Each pathway contains a fast facilitating nonlinearity coupled to a linear response. The linear response is described by an extended log-normal model, accounting for the phasic component. The final nonlinearity is composed of self-inhibition in the UV and green pathways and inhibition between these pathways. The model can largely predict the response of the photoreceptors to UV and green light

Incremental semi-supervised learning for anomalous trajectory detection

The acquisition of a scene-specific normal behaviour model underlies many existing approaches to the problem of automated video surveillance. Since it is unrealistic to acquire a comprehensive set of labelled behaviours for every surveyed scenario, modelling normal behaviour typically corresponds to modelling the distribution of a large collection of unlabelled examples. In general, however, it would be desirable to be able to filter an unlabelled dataset to remove potentially anomalous examples. This thesis proposes a simple semi-supervised learning framework that could allow a human operator to efficiently filter the examples used to construct a normal behaviour model by providing occasional feedback: Specifically, the classification output of the model under construction is used to filter the incoming sequence of unlabelled examples so that human approval is requested before incorporating any example classified as anomalous, while all other examples are automatically used for training. A key component of the proposed framework is an incremental one-class learning algorithm which can be trained on a sequence of normal examples while allowing new examples to be classified at any stage during training. The proposed algorithm represents an initial set of training examples with a kernel density estimate, before using merging operations to incrementally construct a Gaussian mixture model while minimising an information-theoretic cost function. This algorithm is shown to outperform an existing state-of-the-art approach without requiring off-line model selection. Throughout this thesis behaviours are considered in terms of whole motion trajectories: in order to apply the proposed algorithm, trajectories must be encoded with fixed length vectors. To determine an appropriate encoding strategy, an empirical comparison is conducted to determine the relative class-separability afforded by several different trajectory representations for a range of datasets. The results obtained suggest that the choice of representation makes a small but consistent difference to class separability, indicating that cubic B-Spline control points (fitted using least-squares regression) provide a good choice for use in subsequent experiments. The proposed semi-supervised learning framework is tested on three different real trajectory datasets. In all cases the rate of human intervention requests drops steadily, reaching a usefully low level of 1% in one case. A further experiment indicates that once a sufficient number of interventions has been provided, a high level of classification performance can be achieved even if subsequent requests are ignored. The automatic incorporation of unlabelled data is shown to improve classification performance in all cases, while a high level of classification performance is maintained even when unlabelled data containing a high proportion of anomalous examples is presented