Statistical Analysis on Diffusion Tensor Estimation

A thesis submitted in partial fulfilment of the requirements of the University of Wolverhampton for the degree of Doctor of Philosophy.Diffusion tensor imaging (DTI) is a relatively new technology of magnetic resonance imaging, which enables us to observe the insight structure of the human body in vivo and non-invasively. It displays water molecule movement by a 3×3 diffusion tensor at each voxel. Tensor field processing, visualisation and tractography are all based on the diffusion tensors. The accuracy of estimating diffusion tensor is essential in DTI. This research focuses on exploring the potential improvements at the tensor estimation of DTI. We analyse the noise arising in the measurement of diffusion signals. We present robust methods, least median squares (LMS) and least trimmed squares (LTS) regressions, with forward search algorithm that reduce or eliminate outliers to the desired level. An investigation of the criterion to detect outliers is provided in theory and practice. We compare the results with the generalised non-robust models in simulation studies and applicants and also validated various regressions in terms of FA, MD and orientations. We show that the robust methods can handle the data with up to 50% corruption. The robust regressions have better estimations than generalised models in the presence of outliers. We also consider the multiple tensors problems. We review the recent techniques of multiple tensor problems. Then we provide a new model considering neighbours’ information, the Bayesian single and double tensor models using neighbouring tensors as priors, which can identify the double tensors effectively. We design a framework to estimate the diffusion tensor field with detecting whether it is a single tensor model or multiple tensor model. An output of this framework is the Bayesian neighbour (BN) algorithm that improves the accuracy at the intersection of multiple fibres. We examine the dependence of the estimators on the FA and MD and angle between two principal diffusion orientations and the goodness of fit. The Bayesian models are applied to the real data with validation. We show that the double tensors model is more accurate on distinct fibre orientations, more anisotropic or similar mean diffusivity tensors. The final contribution of this research is in covariance tensor estimation. We define the median covariance matrix in terms of Euclidean and various non-Euclidean metrics taking its symmetric semi-positive definiteness into account. We compare with estimation methods, Euclidean, power Euclidean, square root Euclidean, log-Euclidean, Riemannian Euclidean and Procrustes median tensors. We provide an analysis of the different metric between different median covariance tensors. We also provide the weighting functions and define the weighted non-Euclidean covariance tensors. We finish with manifold-valued data applications that improve the illustration of DTI images in tensor field processing with defined non-weighted and weighted median tensors. The validation of non-Euclidean methods is studied in the tensor field processing. We show that the root square median estimator is preferable in general, which can effectively exclude outliers and clearly shows the important structures of the brain. The power Euclidean median estimator is recommended when producing FA map

Stress sensitivity of multiscale pore structure of shale gas reservoir under fracturing fluid imbibition

Generally, huge amounts of fracturing fluid are used in a shale gas well but the flowback efficiency is low. Since the distribution characteristics of imbibed fracturing fluid in shale are complex, they need further evaluation. This paper takes the Longmaxi Shale as the research object, including matrix cores, natural fracture cores and cores of artificial fracture with proppant. Stress sensitivity experiments are carried out on the above three kinds of cores under different degrees of imbibition and retention state of fracturing fluid. The results show that when the degree of aqueous phase retention is 0-0.78 pore volume, water mainly appears in the pores with a diameter of 2-50 nm. As the water saturation increases to more than 0.9 pore volume, the amounts of aqueous phase in the pores or fractures with a hydraulic diameter of 100-1,000 nm and larger than 1,000 nm increase significantly. Both the stress sensitivity of nanopores and natural fractures are enhanced by aqueous phase retention. With the increase in effective stress, the permeability damage rate of artificial fracture cores with proppant is inversely proportional to the degree of fracturing fluid retention. Aqueous phase retention in the pores with a diameter of 2-50 nm significantly contributes to the stress sensitivity of matrix cores. With the increase in effective stress, aqueous phase retention in pores with diameter larger than 100 nm increases the stress sensitivity of natural fracture cores. It is recommended that the retention degree of fracturing fluid in a shale gas reservoir should be controlled below 0.5 pore volume. In this case, the stress sensitivity of natural fractures will be less aggravated by fracturing fluid retention, and the stress sensitivity of artificial fracture with proppant will be reduced to a certain extent.Document Type: Original articleCited as: Chen, M., Yan, M., Kang, Y., Cao, W., Bai, J., Li, P. Stress sensitivity of multiscale pore structure of shale gas reservoir under fracturing fluid imbibition. Capillarity, 2023, 8(1): 11-22. https://doi.org/10.46690/capi.2023.07.0

Orthogonal Temporal Interpolation for Zero-Shot Video Recognition

Zero-shot video recognition (ZSVR) is a task that aims to recognize video categories that have not been seen during the model training process. Recently, vision-language models (VLMs) pre-trained on large-scale image-text pairs have demonstrated impressive transferability for ZSVR. To make VLMs applicable to the video domain, existing methods often use an additional temporal learning module after the image-level encoder to learn the temporal relationships among video frames. Unfortunately, for video from unseen categories, we observe an abnormal phenomenon where the model that uses spatial-temporal feature performs much worse than the model that removes temporal learning module and uses only spatial feature. We conjecture that improper temporal modeling on video disrupts the spatial feature of the video. To verify our hypothesis, we propose Feature Factorization to retain the orthogonal temporal feature of the video and use interpolation to construct refined spatial-temporal feature. The model using appropriately refined spatial-temporal feature performs better than the one using only spatial feature, which verifies the effectiveness of the orthogonal temporal feature for the ZSVR task. Therefore, an Orthogonal Temporal Interpolation module is designed to learn a better refined spatial-temporal video feature during training. Additionally, a Matching Loss is introduced to improve the quality of the orthogonal temporal feature. We propose a model called OTI for ZSVR by employing orthogonal temporal interpolation and the matching loss based on VLMs. The ZSVR accuracies on popular video datasets (i.e., Kinetics-600, UCF101 and HMDB51) show that OTI outperforms the previous state-of-the-art method by a clear margin