Homogeneity based segmentation and enhancement of Diffusion Tensor Images : a white matter processing framework

In diffusion magnetic resonance imaging (DMRI) the Brownian motion of the water molecules, within biological tissue, is measured through a series of images. In diffusion tensor imaging (DTI) this diffusion is represented using tensors. DTI describes, in a non-invasive way, the local anisotropy pattern enabling the reconstruction of the nervous fibers - dubbed tractography. DMRI constitutes a powerful tool to analyse the structure of the white matter within a voxel, but also to investigate the anatomy of the brain and its connectivity. DMRI has been proved useful to characterize brain disorders, to analyse the differences on white matter and consequences in brain function. These procedures usually involve the virtual dissection of white matters tracts of interest. The manual isolation of these bundles requires a great deal of neuroanatomical knowledge and can take up to several hours of work. This thesis focuses on the development of techniques able to automatically perform the identification of white matter structures. To segment such structures in a tensor field, the similarity of diffusion tensors must be assessed for partitioning data into regions, which are homogeneous in terms of tensor characteristics. This concept of tensor homogeneity is explored in order to achieve new methods for segmenting, filtering and enhancing diffusion images. First, this thesis presents a novel approach to semi-automatically define the similarity measures that better suit the data. Following, a multi-resolution watershed framework is presented, where the tensor field’s homogeneity is used to automatically achieve a hierarchical representation of white matter structures in the brain, allowing the simultaneous segmentation of different structures with different sizes. The stochastic process of water diffusion within tissues can be modeled, inferring the homogeneity characteristics of the diffusion field. This thesis presents an accelerated convolution method of diffusion images, where these models enable the contextual processing of diffusion images for noise reduction, regularization and enhancement of structures. These new methods are analysed and compared on the basis of their accuracy, robustness, speed and usability - key points for their application in a clinical setting. The described methods enrich the visualization and exploration of white matter structures, fostering the understanding of the human brain

Variable Splitting as a Key to Efficient Image Reconstruction

The problem of reconstruction of digital images from their degraded measurements has always been a problem of central importance in numerous applications of imaging sciences. In real life, acquired imaging data is typically contaminated by various types of degradation phenomena which are usually related to the imperfections of image acquisition devices and/or environmental effects. Accordingly, given the degraded measurements of an image of interest, the fundamental goal of image reconstruction is to recover its close approximation, thereby "reversing" the effect of image degradation. Moreover, the massive production and proliferation of digital data across different fields of applied sciences creates the need for methods of image restoration which would be both accurate and computationally efficient. Developing such methods, however, has never been a trivial task, as improving the accuracy of image reconstruction is generally achieved at the expense of an elevated computational burden. Accordingly, the main goal of this thesis has been to develop an analytical framework which allows one to tackle a wide scope of image reconstruction problems in a computationally efficient manner. To this end, we generalize the concept of variable splitting, as a tool for simplifying complex reconstruction problems through their replacement by a sequence of simpler and therefore easily solvable ones. Moreover, we consider two different types of variable splitting and demonstrate their connection to a number of existing approaches which are currently used to solve various inverse problems. In particular, we refer to the first type of variable splitting as Bregman Type Splitting (BTS) and demonstrate its applicability to the solution of complex reconstruction problems with composite, cross-domain constraints. As specific applications of practical importance, we consider the problem of reconstruction of diffusion MRI signals from sub-critically sampled, incomplete data as well as the problem of blind deconvolution of medical ultrasound images. Further, we refer to the second type of variable splitting as Fuzzy Clustering Splitting (FCS) and show its application to the problem of image denoising. Specifically, we demonstrate how this splitting technique allows us to generalize the concept of neighbourhood operation as well as to derive a unifying approach to denoising of imaging data under a variety of different noise scenarios

Global tractography with embedded anatomical priors for quantitative connectivity analysis.

Tractography algorithms provide us with the ability to non-invasively reconstruct fiber pathways in the white matter (WM) by exploiting the directional information described with diffusion magnetic resonance. These methods could be divided into two major classes, local and global. Local methods reconstruct each fiber tract iteratively by considering only directional information at the voxel level and its neighborhood. Global methods, on the other hand, reconstruct all the fiber tracts of the whole brain simultaneously by solving a global energy minimization problem. The latter have shown improvements compared to previous techniques but these algorithms still suffer from an important shortcoming that is crucial in the context of brain connectivity analyses. As no anatomical priors are usually considered during the reconstruction process, the recovered fiber tracts are not guaranteed to connect cortical regions and, as a matter of fact, most of them stop prematurely in the WM; this violates important properties of neural connections, which are known to originate in the gray matter (GM) and develop in the WM. Hence, this shortcoming poses serious limitations for the use of these techniques for the assessment of the structural connectivity between brain regions and, de facto, it can potentially bias any subsequent analysis. Moreover, the estimated tracts are not quantitative, every fiber contributes with the same weight toward the predicted diffusion signal. In this work, we propose a novel approach for global tractography that is specifically designed for connectivity analysis applications which: (i) explicitly enforces anatomical priors of the tracts in the optimization and (ii) considers the effective contribution of each of them, i.e., volume, to the acquired diffusion magnetic resonance imaging (MRI) image. We evaluated our approach on both a realistic diffusion MRI phantom and in vivo data, and also compared its performance to existing tractography algorithms

Moment-based representation of the diffusion inside the brain from reduced DMRI acquisitions: Generalized AMURA

Producción CientíficaAMURA (Apparent Measures Using Reduced Acquisitions) was originally proposed as a method to infer micro-structural information from single-shell acquisitions in diffusion MRI. It reduces the number of samples needed and the computational complexity of the estimation of diffusion properties of tissues by assuming the diffusion anisotropy is roughly independent on the b-value. This simplification allows the computation of simplified expressions and makes it compatible with standard acquisition protocols commonly used even in clinical practice. The present work proposes an extension of AMURA that allows the calculation of general moments of the diffusion signals that can be applied to describe the diffusion process with higher accuracy. We provide simplified expressions to analytically compute a set of scalar indices as moments of arbitrary orders over either the whole 3-D space, particular directions, or particular planes. The existing metrics previously proposed for AMURA (RTOP, RTPP and RTAP) are now special cases of this generalization. An extensive set of experiments is performed on public data and a clinical clase acquired with a standard type acquisition. The new metrics provide additional information about the diffusion processes inside the brain.Ministerio de Ciencia, Innovación y Universidades (grant RTI2018-094569-B-I00)Polish National Agency for Academic Exchange (grant PN/BEK/2019/1/00421)Ministry of Science and Higher Education of Poland (scholarship 692/STYP/13/2018)Junta de Castilla y León - Fondo Social Europeo (ID: 376062

Micro-structure diffusion scalar measures from reduced MRI acquisitions

In diffusion MRI, the Ensemble Average diffusion Propagator (EAP) provides relevant microstructural information and meaningful descriptive maps of the white matter previously obscured by traditional techniques like the Diffusion Tensor. The direct estimation of the EAP, however, requires a dense sampling of the Cartesian q-space. Due to the huge amount of samples needed for an accurate reconstruction, more efficient alternative techniques have been proposed in the last decade. Even so, all of them imply acquiring a large number of diffusion gradients with different b-values. In order to use the EAP in practical studies, scalar measures must be directly derived, being the most common the return-to-origin probability (RTOP) and the return-to-plane and return-to-axis probabilities (RTPP, RTAP). In this work, we propose the so-called “Apparent Measures Using Reduced Acquisitions” (AMURA) to drastically reduce the number of samples needed for the estimation of diffusion properties. AMURA avoids the calculation of the whole EAP by assuming the diffusion anisotropy is roughly independent from the radial direction. With such an assumption, and as opposed to common multi-shell procedures based on iterative optimization, we achieve closed-form expressions for the measures using information from one single shell. This way, the new methodology remains compatible with standard acquisition protocols commonly used for HARDI (based on just one b-value). We report extensive results showing the potential of AMURA to reveal microstructural properties of the tissues compared to state of the art EAP estimators, and is well above that of Diffusion Tensor techniques. At the same time, the closed forms provided for RTOP, RTPP, and RTAP-like magnitudes make AMURA both computationally efficient and robust

Extraction of Structural Metrics from Crossing Fiber Models

Diffusion MRI (dMRI) measurements allow us to infer the microstructural properties of white matter and to reconstruct fiber pathways in-vivo. High angular diffusion imaging (HARDI) allows for the creation of more and more complex local models connecting the microstructure to the measured signal. One of the challenges is the derivation of meaningful metrics describing the underlying structure from the local models. The aim hereby is to increase the specificity of the widely used metric fractional anisotropy (FA) by using the additional information contained within the HARDI data. A local model which is connected directly to the underlying microstructure through the model of a single fiber population is spherical deconvolution. It produces a fiber orientation density function (fODF), which can often be interpreted as superposition of multiple peaks, each associated to one relatively coherent fiber population (bundle). Parameterizing these peaks one is able to disentangle and characterize these bundles. In this work, the fODF peaks are approximated by Bingham distributions, capturing first and second order statistics of the fiber orientations, from which metrics for the parametric quantification of fiber bundles are derived. Meaningful relationships between these measures and the underlying microstructural properties are proposed. The focus lies on metrics derived directly from properties of the Bingham distribution, such as peak length, peak direction, peak spread, integral over the peak, as well as a metric derived from the comparison of the largest peaks, which probes the complexity of the underlying microstructure. These metrics are compared to the conventionally used fractional anisotropy (FA) and it is shown how they may help to increase the specificity of the characterization of microstructural properties. Visualization of the micro-structural arrangement is another application of dMRI. This is done by using tractography to propagate the fiber layout, extracted from the local model, in each voxel. In practice most tractography algorithms use little of the additional information gained from HARDI based local models aside from the reconstructed fiber bundle directions. In this work an approach to tractography based on the Bingham parameterization of the fODF is introduced. For each of the fiber populations present in a voxel the diffusion signal and tensor are computed. Then tensor deflection tractography is performed. This allows incorporating the complete bundle information, performing local interpolation as well as using multiple directions per voxel for generating tracts. Another aspect of this work is the investigation of the spherical harmonic representation which is used most commonly for the fODF by means of the parameters derived from the Bingham distribution fit. Here a strong connection between the approximation errors in the spherical representation of the Dirac delta function and the distribution of crossing angles recovered from the fODF was discovered. The final aspect of this work is the application of the metrics derived from the Bingham fit to a number of fetal datasets for quantifying the brain’s development. This is done by introducing the Gini-coefficient as a metric describing the brain’s age

Joint Spatial-Angular Sparse Coding, Compressed Sensing, and Dictionary Learning for Diffusion MRI

Neuroimaging provides a window into the inner workings of the human brain to diagnose and prevent neurological diseases and understand biological brain function, anatomy, and psychology. Diffusion Magnetic Resonance Imaging (dMRI) is an emerging medical imaging modality used to study the anatomical network of neurons in the brain, which form cohesive bundles, or fiber tracts, that connect various parts of the brain. Since about 73% of the brain is water, measuring the flow, or diffusion of water molecules in the presence of fiber bundles, allows researchers to estimate the orientation of fiber tracts and reconstruct the internal wiring of the brain, in vivo. Diffusion MRI signals can be modeled within two domains: the spatial domain consisting of voxels in a brain volume and the diffusion or angular domain, where fiber orientation is estimated in each voxel. Researchers aim to estimate the probability distribution of fiber orientation in every voxel of a brain volume in order to trace paths of fiber tracts from voxel to voxel over the entire brain. Therefore, the traditional framework for dMRI processing and analysis has been from a voxel-wise vantage point with added spatial regularization considered post-hoc. In contrast, we propose a new joint spatial-angular representation of dMRI data which pairs signals in each voxel with the global spatial environment, jointly. This has the ability to improve many aspects of dMRI processing and analysis and re-envision the core representation of dMRI data from a local perspective to a global one. In this thesis, we propose three main contributions which take advantage of such joint spatial-angular representations to improve major machine learning tasks applied to dMRI: sparse coding, compressed sensing, and dictionary learning. First, we will show that we can achieve sparser representations of dMRI by utilizing a global spatial-angular dictionary instead of a purely voxel-wise angular dictionary. As dMRI data is very large in size, we provide a number of novel extensions to popular spare coding algorithms that perform efficient optimization on a global-scale by exploiting the separability of our dictionaries over the spatial and angular domains. Next, compressed sensing is used to accelerate signal acquisition based on an underlying sparse representation of the data. We will show that our proposed representation has the potential to push the limits of the current state of scanner acceleration within a new compressed sensing model for dMRI. Finally, sparsity can be further increased by learning dictionaries directly from datasets of interest. Prior dictionary learning for dMRI learn angular dictionaries alone. Our third contribution is to learn spatial-angular dictionaries jointly from dMRI data directly to better represent the global structure. Traditionally, the problem of dictionary learning is non-convex with no guarantees of finding a globally optimal solution. We derive the first theoretical results of global optimality for this class of dictionary learning problems. We hope the core foundation of a joint spatial-angular representation will open a new perspective on dMRI with respect to many other processing tasks and analyses. In addition, our contributions are applicable to any general signal types that can benefit from separable dictionaries. We hope the contributions in this thesis may be adopted in the larger signal processing, computer vision, and machine learning communities. dMRI signals can be modeled within two domains: the spatial domain consisting of voxels in a brain volume and the diffusion or angular domain, where fiber orientation is estimated in each voxel. Computationally speaking, researchers aim to estimate the probability distribution of fiber orientation in every voxel of a brain volume in order to trace paths of fiber tracts from voxel to voxel over the entire brain. Therefore, the traditional framework for dMRI processing and analysis is from a voxel-wise, or angular, vantage point with post-hoc consideration of their local spatial neighborhoods. In contrast, we propose a new global spatial-angular representation of dMRI data which pairs signals in each voxel with the global spatial environment, jointly, to improve many aspects of dMRI processing and analysis, including the important need for accelerating the otherwise time-consuming acquisition of advanced dMRI protocols. In this thesis, we propose three main contributions which utilize our joint spatial-angular representation to improve major machine learning tasks applied to dMRI: sparse coding, compressed sensing, and dictionary learning. We will show that sparser codes are possible by utilizing a global dictionary instead of a voxel-wise angular dictionary. This allows for a reduction of the number of measurements needed to reconstruct a dMRI signal to increase acceleration using compressed sensing. Finally, instead of learning angular dictionaries alone, we learn spatial-angular dictionaries jointly from dMRI data directly to better represent the global structure. In addition, this problem is non-convex and so we derive the first theories to guarantee convergence to a global minimum. As dMRI data is very large in size, we provide a number of novel extensions to popular algorithms that perform efficient optimization on a global-scale by exploiting the separability of our global dictionaries over the spatial and angular domains. We hope the core foundation of a joint spatial-angular representation will open a new perspective on dMRI with respect to many other processing tasks and analyses. In addition, our contributions are applicable to any separable dictionary setting which we hope may be adopted in the larger image processing, computer vision, and machine learning communities

Anisotropy Across Fields and Scales

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018