Akram Aldroubi

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Fiber tract trajectories in coherently organized brain white matter pathways were computed from in vivo diffusion tensor magnetic resonance imaging (DT-MRI) data. First, a continuous diffusion tensor field is constructed from this discrete, noisy, measured DT-MRI data. Then a Frenet equation, describing the evolution of a fiber tract, was solved. This(More)
This article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift-invariant spaces. It is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shiftinvariant spaces by bringing together wavelet theory, frame theory, reproducing kernel Hilbert(More)
Nonrigid registration of medical images is important for a number of applications such as the creation of population averages, atlas-based segmentation, or geometric correction of functional magnetic resonance imaging (fMRI) images to name a few. In recent years, a number of methods have been proposed to solve this problem, one class of which involves(More)
The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical(More)
Under the appropriate definition of sampling density Dφ, a function f that belongs to a shift invariant space can be reconstructed in a stable way from its non-uniform samples only if Dφ ≥ 1. This result is similar to Landau’s result for the PaleyWiener space B1/2. If the shift invariant space consists of polynomial splines, then we show that Dφ < 1 is(More)