Estimation of Fiber Orientations Using Neighborhood Information

Data from diffusion magnetic resonance imaging (dMRI) can be used to reconstruct fiber tracts, for example, in muscle and white matter. Estimation of fiber orientations (FOs) is a crucial step in the reconstruction process and these estimates can be corrupted by noise. In this paper, a new method called Fiber Orientation Reconstruction using Neighborhood Information (FORNI) is described and shown to reduce the effects of noise and improve FO estimation performance by incorporating spatial consistency. FORNI uses a fixed tensor basis to model the diffusion weighted signals, which has the advantage of providing an explicit relationship between the basis vectors and the FOs. FO spatial coherence is encouraged using weighted l1-norm regularization terms, which contain the interaction of directional information between neighbor voxels. Data fidelity is encouraged using a squared error between the observed and reconstructed diffusion weighted signals. After appropriate weighting of these competing objectives, the resulting objective function is minimized using a block coordinate descent algorithm, and a straightforward parallelization strategy is used to speed up processing. Experiments were performed on a digital crossing phantom, ex vivo tongue dMRI data, and in vivo brain dMRI data for both qualitative and quantitative evaluation. The results demonstrate that FORNI improves the quality of FO estimation over other state of the art algorithms.Comment: Journal paper accepted in Medical Image Analysis. 35 pages and 16 figure

Fast Optimal Transport Averaging of Neuroimaging Data

Knowing how the Human brain is anatomically and functionally organized at the level of a group of healthy individuals or patients is the primary goal of neuroimaging research. Yet computing an average of brain imaging data defined over a voxel grid or a triangulation remains a challenge. Data are large, the geometry of the brain is complex and the between subjects variability leads to spatially or temporally non-overlapping effects of interest. To address the problem of variability, data are commonly smoothed before group linear averaging. In this work we build on ideas originally introduced by Kantorovich to propose a new algorithm that can average efficiently non-normalized data defined over arbitrary discrete domains using transportation metrics. We show how Kantorovich means can be linked to Wasserstein barycenters in order to take advantage of an entropic smoothing approach. It leads to a smooth convex optimization problem and an algorithm with strong convergence guarantees. We illustrate the versatility of this tool and its empirical behavior on functional neuroimaging data, functional MRI and magnetoencephalography (MEG) source estimates, defined on voxel grids and triangulations of the folded cortical surface.Comment: Information Processing in Medical Imaging (IPMI), Jun 2015, Isle of Skye, United Kingdom. Springer, 201

Mathematical Modeling of the Human Brain

This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain

Model-Based Visualization for Intervention Planning

Computer support for intervention planning is often a two-stage process: In a first stage, the relevant segmentation target structures are identified and delineated. In a second stage, image analysis results are employed for the actual planning process. In the first stage, model-based segmentation techniques are often used to reduce the interaction effort and increase the reproducibility. There is a similar argument to employ model-based techniques for the visualization as well. With increasingly more visualization options, users have many parameters to adjust in order to generate expressive visualizations. Surface models may be smoothed with a variety of techniques and parameters. Surface visualization and illustrative rendering techniques are controlled by a large set of additional parameters. Although interactive 3d visualizations should be flexible and support individual planning tasks, appropriate selection of visualization techniques and presets for their parameters is needed. In this chapter, we discuss this kind of visualization support. We refer to model-based visualization to denote the selection and parameterization of visualization techniques based on \u27a priori knowledge concerning visual perception, shapes of anatomical objects and intervention planning tasks

Mathematical Modeling of the Human Brain

This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain

Nonlinear tube-fitting for the analysis of anatomical and functional structures

We are concerned with the estimation of the exterior surface and interior summaries of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT) and to a white-matter tract image produced using diffusion tensor imaging (DTI).Comment: Published in at http://dx.doi.org/10.1214/10-AOAS384 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Role of deep learning techniques in non-invasive diagnosis of human diseases.

Machine learning, a sub-discipline in the domain of artificial intelligence, concentrates on algorithms able to learn and/or adapt their structure (e.g., parameters) based on a set of observed data. The adaptation is performed by optimizing over a cost function. Machine learning obtained a great attention in the biomedical community because it offers a promise for improving sensitivity and/or specificity of detection and diagnosis of diseases. It also can increase objectivity of the decision making, decrease the time and effort on health care professionals during the process of disease detection and diagnosis. The potential impact of machine learning is greater than ever due to the increase in medical data being acquired, the presence of novel modalities being developed and the complexity of medical data. In all of these scenarios, machine learning can come up with new tools for interpreting the complex datasets that confront clinicians. Much of the excitement for the application of machine learning to biomedical research comes from the development of deep learning which is modeled after computation in the brain. Deep learning can help in attaining insights that would be impossible to obtain through manual analysis. Deep learning algorithms and in particular convolutional neural networks are different from traditional machine learning approaches. Deep learning algorithms are known by their ability to learn complex representations to enhance pattern recognition from raw data. On the other hand, traditional machine learning requires human engineering and domain expertise to design feature extractors and structure data. With increasing demands upon current radiologists, there are growing needs for automating the diagnosis. This is a concern that deep learning is able to address. In this dissertation, we present four different successful applications of deep learning for diseases diagnosis. All the work presented in the dissertation utilizes medical images. In the first application, we introduce a deep-learning based computer-aided diagnostic system for the early detection of acute renal transplant rejection. The system is based on the fusion of both imaging markers (apparent diffusion coefficients derived from diffusion-weighted magnetic resonance imaging) and clinical biomarkers (creatinine clearance and serum plasma creatinine). The fused data is then used as an input to train and test a convolutional neural network based classifier. The proposed system is tested on scans collected from 56 subjects from geographically diverse populations and different scanner types/image collection protocols. The overall accuracy of the proposed system is 92.9% with 93.3% sensitivity and 92.3% specificity in distinguishing non-rejected kidney transplants from rejected ones. In the second application, we propose a novel deep learning approach for the automated segmentation and quantification of the LV from cardiac cine MR images. We aimed at achieving lower errors for the estimated heart parameters compared to the previous studies by proposing a novel deep learning segmentation method. Using fully convolutional neural networks, we proposed novel methods for the extraction of a region of interest that contains the left ventricle, and the segmentation of the left ventricle. Following myocardial segmentation, functional and mass parameters of the left ventricle are estimated. Automated Cardiac Diagnosis Challenge dataset was used to validate our framework, which gave better segmentation, accurate estimation of cardiac parameters, and produced less error compared to other methods applied on the same dataset. Furthermore, we showed that our segmentation approach generalizes well across different datasets by testing its performance on a locally acquired dataset. In the third application, we propose a novel deep learning approach for automated quantification of strain from cardiac cine MR images of mice. For strain analysis, we developed a Laplace-based approach to track the LV wall points by solving the Laplace equation between the LV contours of each two successive image frames over the cardiac cycle. Following tracking, the strain estimation is performed using the Lagrangian-based approach. This new automated system for strain analysis was validated by comparing the outcome of these analysis with the tagged MR images from the same mice. There were no significant differences between the strain data obtained from our algorithm using cine compared to tagged MR imaging. In the fourth application, we demonstrate how a deep learning approach can be utilized for the automated classification of kidney histopathological images. Our approach can classify four classes: the fat, the parenchyma, the clear cell renal cell carcinoma, and the unusual cancer which has been discovered recently, called clear cell papillary renal cell carcinoma. Our framework consists of three convolutional neural networks and the whole-slide kidney images were divided into patches with three different sizes to be inputted to the networks. Our approach can provide patch-wise and pixel-wise classification. Our approach classified the four classes accurately and surpassed other state-of-the-art methods such as ResNet (pixel accuracy: 0.89 Resnet18, 0.93 proposed). In conclusion, the results of our proposed systems demonstrate the potential of deep learning for the efficient, reproducible, fast, and affordable disease diagnosis

Sampling Sparse Signals on the Sphere: Algorithms and Applications

We propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass-filtered observations. Central to our algorithm is a generalization of the annihilating filter method, a tool widely used in array signal processing and finite-rate-of-innovation (FRI) sampling. The proposed algorithm can reconstruct $K$ spikes from $(K+\sqrt{K})^2$ spatial samples. This sampling requirement improves over previously known FRI sampling schemes on the sphere by a factor of four for large $K$. We showcase the versatility of the proposed algorithm by applying it to three different problems: 1) sampling diffusion processes induced by localized sources on the sphere, 2) shot noise removal, and 3) sound source localization (SSL) by a spherical microphone array. In particular, we show how SSL can be reformulated as a spherical sparse sampling problem.Comment: 14 pages, 8 figures, submitted to IEEE Transactions on Signal Processin

Higher-order image statistics for unsupervised, information-theoretic, adaptive, image filtering

technical reportThe restoration of images is an important and widely studied problem in computer vision and image processing. Various image filtering strategies have been effective, but invariably make strong assumptions about the properties of the signal and/or degradation. Therefore, these methods typically lack the generality to be easily applied to new applications or diverse image collections. This paper describes a novel unsupervised, informationtheoretic, adaptive filter (UINTA) that improves the predictability of pixel intensities from their neighborhoods by decreasing the joint entropy between them. Thus UINTA automatically discovers the statistical properties of the signal and can thereby restore a wide spectrum of images and applications. This paper describes the formulation required to minimize the joint entropy measure, presents several important practical considerations in estimating image-region statistics, and then presents results on both real and synthetic data