Unsupervised Frequency Tracking beyond the Nyquist Limit using Markov Chains

This paper deals with the estimation of a sequence of frequencies from a corresponding sequence of signals. This problem arises in fields such as Doppler imaging where its specificity is twofold. First, only short noisy data records are available (typically four sample long) and experimental constraints may cause spectral aliasing so that measurements provide unreliable, ambiguous information. Second, the frequency sequence is smooth. Here, this information is accounted for by a Markov model and application of the Bayes rule yields the a posteriori density. The maximum a postariori is computed by a combination of Viterbi and descent procedures. One of the major features of the method is that it is entirely unsupervised. Adjusting the hyperparameters that balance data-based and prior-based information is done automatically by ML using an EM-based gradient algorithm. We compared the proposed estimate to a reference one and found that it performed better: variance was greatly reduced and tracking was correct, even beyond the Nyquist frequency

Towards efficient neurosurgery: Image analysis for interventional MRI

Interventional magnetic resonance imaging (iMRI) is being increasingly used for performing imageguided neurosurgical procedures. Intermittent imaging through iMRI can help a neurosurgeon visualise the target and eloquent brain areas during neurosurgery and lead to better patient outcome. MRI plays an important role in planning and performing neurosurgical procedures because it can provide highresolution anatomical images that can be used to discriminate between healthy and diseased tissue, as well as identify location and extent of functional areas. This is of significant clinical utility as it helps the surgeons maximise target resection and avoid damage to functionally important brain areas. There is clinical interest in propagating the pre-operative surgical information to the intra-operative image space as this allows the surgeons to utilise the pre-operatively generated surgical plans during surgery. The current state of the art neuronavigation systems achieve this by performing rigid registration of pre-operative and intra-operative images. As the brain undergoes non-linear deformations after craniotomy (brain shift), the rigidly registered pre-operative images do not accurately align anymore with the intra-operative images acquired during surgery. This limits the accuracy of these neuronavigation systems and hampers the surgeon’s ability to perform more aggressive interventions. In addition, intra-operative images are typically of lower quality with susceptibility artefacts inducing severe geometric and intensity distortions around areas of resection in echo planar MRI images, significantly reducing their utility in the intraoperative setting. This thesis focuses on development of novel methods for an image processing workflow that aims to maximise the utility of iMRI in neurosurgery. I present a fast, non-rigid registration algorithm that can leverage information from both structural and diffusion weighted MRI images to localise target lesions and a critical white matter tract, the optic radiation, during surgical management of temporal lobe epilepsy. A novel method for correcting susceptibility artefacts in echo planar MRI images is also developed, which combines fieldmap and image registration based correction techniques. The work developed in this thesis has been validated and successfully integrated into the surgical workflow at the National Hospital for Neurology and Neurosurgery in London and is being clinically used to inform surgical decisions

Functional Sampling Tool: A Novel Method to Enhance Sampling in Molecular Dynamics Simulations : with applications to NMDAR dynamics

NMDA receptors are ionotropic glutamate receptors (iGluRs), tetrameric proteins, mediating synaptic transmission in the brain and the whole nervous system. Together with another type of iGluRs, AMPA receptors, they are considered essential for neuronal plasticity and memory. Understanding their dynamics and different kinetics is vital for studying various neurological diseases. The relatively slow dynamics, where the time scales of related processes range up to hundreds of milliseconds, make studying them with Molecular Dynamics (MD) simulations challenging. We developed the Functional Sampling Tool (FST), a novel method for enhancing the sampling of a function of interest. Compared to existing enhanced sampling schemes it strikes a balance between generality and simplicity, minimising the need of user input, while allowing for maximal customisability. Using FST, we studied two processes of the NMDA receptor. By keeping all four ligands bound we simulated a desensitisation pathway, and by removing all four we simulated an inactivation pathway. The tool sampled both, giving a good distribution between open and closed states. The tool also allowed us to change the function in the middle of sampling. With the new function we were able to produce more data, focusing on a certain value range

Quantifying Oil and Gas Industry Related Geohazard Using Radar Interferometry and Hydro-geomechanical Modeling

The Permian Basin, containing a large amount of oil and gas, has been intensively developed for hydrocarbon production. However, the hazards related to the oil and gas industry including surface deformation and the underlying mechanisms in this region have not been well known. My PhD study aims to monitor the geohazards in the Permian Basin and better comprehend the subsurface mechanisms with the aid of high-resolution and high-accuracy Interferometric Synthetic Aperture Radar (InSAR) images. Generally, as the pore pressure is influenced by wastewater injection/hydrocarbon production, the pressure changes can propagate to other surrounding underground and overlying rock/soil layers, resulting in surface deformation. The distribution and temporal development of the surface deformation can be obtained from InSAR processing and analysis. To reveal the underground geo-mechanical process responsible for the development of the surface deformation, numerical modeling based on poroelasticity is then applied to estimate the effective parameters (i.e., parameters inferred from the simulation) including depth and volume. This method is applied to three cases in West Texas. At a site in Reeves county, InSAR detects surface uplift up to 17 cm near a wastewater disposal well from 2007 to 2011. Results from both elastic and poroelastic models indicate that the effective injection depth is much shallower than reported. The most reasonable explanation is that the well was experiencing leakage due to casing failures and/or sealing problem(s). At a site in Winkler county, surface uplift and the follow-on recovery detected by InSAR from 2015 to 2020 can be attributed to nearby wastewater disposal. Bayesian inversion with the poroelastic models provides estimates of the local hydro-geomechanical parameters. The posterior distribution of subsurface effective volumes reveals under-reported volumes in the well near the deformation center. We also investigate a case of aseismic slip related to oil and gas activities. The combination of InSAR observation and poroelastic finite element models in three cases shows the capability to investigate the ongoing geohazards related to fluid injection and hydrocarbon production in the Permian Basin. This kind of study will be helpful to the decision-making of federal/local authorities to avoid future geohazards related to oil and gas activities

Inverse problems in medical ultrasound images - applications to image deconvolution, segmentation and super-resolution

In the field of medical image analysis, ultrasound is a core imaging modality employed due to its real time and easy-to-use nature, its non-ionizing and low cost characteristics. Ultrasound imaging is used in numerous clinical applications, such as fetus monitoring, diagnosis of cardiac diseases, flow estimation, etc. Classical applications in ultrasound imaging involve tissue characterization, tissue motion estimation or image quality enhancement (contrast, resolution, signal to noise ratio). However, one of the major problems with ultrasound images, is the presence of noise, having the form of a granular pattern, called speckle. The speckle noise in ultrasound images leads to the relative poor image qualities compared with other medical image modalities, which limits the applications of medical ultrasound imaging. In order to better understand and analyze ultrasound images, several device-based techniques have been developed during last 20 years. The object of this PhD thesis is to propose new image processing methods allowing us to improve ultrasound image quality using postprocessing techniques. First, we propose a Bayesian method for joint deconvolution and segmentation of ultrasound images based on their tight relationship. The problem is formulated as an inverse problem that is solved within a Bayesian framework. Due to the intractability of the posterior distribution associated with the proposed Bayesian model, we investigate a Markov chain Monte Carlo (MCMC) technique which generates samples distributed according to the posterior and use these samples to build estimators of the ultrasound image. In a second step, we propose a fast single image super-resolution framework using a new analytical solution to the l2-l2 problems (i.e., $\ell_2$-norm regularized quadratic problems), which is applicable for both medical ultrasound images and piecewise/ natural images. In a third step, blind deconvolution of ultrasound images is studied by considering the following two strategies: i) A Gaussian prior for the PSF is proposed in a Bayesian framework. ii) An alternating optimization method is explored for blind deconvolution of ultrasound

Temporally Coherent Backmapping of Molecular Trajectories From Coarse-Grained to Atomistic Resolution

Coarse-graining offers a means to extend the achievable time and length scales of molecular dynamics simulations beyond what is practically possible in the atomistic regime. Sampling molecular configurations of interest can be done efficiently using coarse-grained simulations, from which meaningful physicochemical information can be inferred if the corresponding all-atom configurations are reconstructed. However, this procedure of backmapping to reintroduce the lost atomistic detail into coarse-grain structures has proven a challenging task due to the many feasible atomistic configurations that can be associated with one coarse-grain structure. Existing backmapping methods are strictly frame-based, relying on either heuristics to replace coarse-grain particles with atomic fragments and subsequent relaxation or parametrized models to propose atomic coordinates separately and independently for each coarse-grain structure. These approaches neglect information from previous trajectory frames that is critical to ensuring temporal coherence of the backmapped trajectory, while also offering information potentially helpful to producing higher-fidelity atomic reconstructions. In this work, we present a deep learning-enabled data-driven approach for temporally coherent backmapping that explicitly incorporates information from preceding trajectory structures. Our method trains a conditional variational autoencoder to nondeterministically reconstruct atomistic detail conditioned on both the target coarse-grain configuration and the previously reconstructed atomistic configuration. We demonstrate our backmapping approach on two exemplar biomolecular systems: alanine dipeptide and the miniprotein chignolin. We show that our backmapped trajectories accurately recover the structural, thermodynamic, and kinetic properties of the atomistic trajectory data