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 Fiber Orientation Estimation in Diffusion MRI from kq-Space Sampling and Anatomical Priors

High spatio-angular resolution diffusion MRI (dMRI) has been shown to provide accurate identification of complex fiber configurations, albeit at the cost of long acquisition times. We propose a method to recover intra-voxel fiber configurations at high spatio-angular resolution relying on a kq-space under-sampling scheme to enable accelerated acquisitions. The inverse problem for reconstruction of the fiber orientation distribution (FOD) is regularized by a structured sparsity prior promoting simultaneously voxelwise sparsity and spatial smoothness of fiber orientation. Prior knowledge of the spatial distribution of white matter, gray matter and cerebrospinal fluid is also assumed. A minimization problem is formulated and solved via a forward-backward convex optimization algorithmic structure. Simulations and real data analysis suggest that accurate FOD mapping can be achieved from severe kq-space under-sampling regimes, potentially enabling high spatio-angular dMRI in the clinical setting.Comment: 10 pages, 5 figures, Supplementary Material

The Filament Sensor for Near Real-Time Detection of Cytoskeletal Fiber Structures

A reliable extraction of filament data from microscopic images is of high interest in the analysis of acto-myosin structures as early morphological markers in mechanically guided differentiation of human mesenchymal stem cells and the understanding of the underlying fiber arrangement processes. In this paper, we propose the filament sensor (FS), a fast and robust processing sequence which detects and records location, orientation, length and width for each single filament of an image, and thus allows for the above described analysis. The extraction of these features has previously not been possible with existing methods. We evaluate the performance of the proposed FS in terms of accuracy and speed in comparison to three existing methods with respect to their limited output. Further, we provide a benchmark dataset of real cell images along with filaments manually marked by a human expert as well as simulated benchmark images. The FS clearly outperforms existing methods in terms of computational runtime and filament extraction accuracy. The implementation of the FS and the benchmark database are available as open source.Comment: 32 pages, 21 figure

Angular Upsampling in Infant Diffusion MRI Using Neighborhood Matching in x-q Space

Diffusion MRI requires sufficient coverage of the diffusion wavevector space, also known as the q-space, to adequately capture the pattern of water diffusion in various directions and scales. As a result, the acquisition time can be prohibitive for individuals who are unable to stay still in the scanner for an extensive period of time, such as infants. To address this problem, in this paper we harness non-local self-similar information in the x-q space of diffusion MRI data for q-space upsampling. Specifically, we first perform neighborhood matching to establish the relationships of signals in x-q space. The signal relationships are then used to regularize an ill-posed inverse problem related to the estimation of high angular resolution diffusion MRI data from its low-resolution counterpart. Our framework allows information from curved white matter structures to be used for effective regularization of the otherwise ill-posed problem. Extensive evaluations using synthetic and infant diffusion MRI data demonstrate the effectiveness of our method. Compared with the widely adopted interpolation methods using spherical radial basis functions and spherical harmonics, our method is able to produce high angular resolution diffusion MRI data with greater quality, both qualitatively and quantitatively.Comment: 15 pages, 12 figure

An Infinitesimal Probabilistic Model for Principal Component Analysis of Manifold Valued Data

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean PCA procedure, we show how PCA can be generalized to manifolds in an intrinsic way that does not resort to linearization of the data space. The underlying probability model is constructed by mapping a Euclidean stochastic process to the manifold using stochastic development of Euclidean semimartingales. The construction uses a connection and bundles of covariant tensors to allow global transport of principal eigenvectors, and the model is thereby an example of how principal fiber bundles can be used to handle the lack of global coordinate system and orientations that characterizes manifold valued statistics. We show how curvature implies non-integrability of the equivalent of Euclidean principal subspaces, and how the stochastic flows provide an alternative to explicit construction of such subspaces. We describe estimation procedures for inference of parameters and prediction of principal components, and we give examples of properties of the model on embedded surfaces

Learning-based Ensemble Average Propagator Estimation

By capturing the anisotropic water diffusion in tissue, diffusion magnetic resonance imaging (dMRI) provides a unique tool for noninvasively probing the tissue microstructure and orientation in the human brain. The diffusion profile can be described by the ensemble average propagator (EAP), which is inferred from observed diffusion signals. However, accurate EAP estimation using the number of diffusion gradients that is clinically practical can be challenging. In this work, we propose a deep learning algorithm for EAP estimation, which is named learning-based ensemble average propagator estimation (LEAPE). The EAP is commonly represented by a basis and its associated coefficients, and here we choose the SHORE basis and design a deep network to estimate the coefficients. The network comprises two cascaded components. The first component is a multiple layer perceptron (MLP) that simultaneously predicts the unknown coefficients. However, typical training loss functions, such as mean squared errors, may not properly represent the geometry of the possibly non-Euclidean space of the coefficients, which in particular causes problems for the extraction of directional information from the EAP. Therefore, to regularize the training, in the second component we compute an auxiliary output of approximated fiber orientation (FO) errors with the aid of a second MLP that is trained separately. We performed experiments using dMRI data that resemble clinically achievable $q$-space sampling, and observed promising results compared with the conventional EAP estimation method.Comment: Accepted by MICCAI 201