Recent development in sampling theory now allows the sampling and reconstruction of certain non-bandlimited functions on the sphere, namely a sum of weighted Diracs. Because the signal acquired in diffusion Magnetic Resonance Imaging (dMRI) can be modeled as the convolution between a sampling kernel and two dimensional Diracs defined on the sphere, these advances have great potential in dMRI. I...

Numerical deconvolution of 3D fluorescence microscopy data yields sharper images by reversing the known optical aberrations introduced during the acquisition process. When additional prior information such as the topology and smoothness of the imaged object surface is available, the deconvolution can be performed by fitting a parametric surface directly to the image data. In this work, we incor...

We report on the initial results obtained with an image convolution/deconvolution computer code that we developed and used to study formation capabilities of solar gravitational lens (SGL). Although SGL a spherical Sun creates greatly blurred image, knowledge SGL's point-spread function (PSF) makes it possible reconstruct original remove blur by way deconvolution. discuss deconvolution process,...

Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR-SD),...

Spherical deconvolution models the diffusion MRI signal as the convolution of a fiber orientation density function (fODF) with a single fiber response. We propose a novel calibration procedure that automatically determines this fiber response. This has three advantages: First, the user no longer needs to provide an estimate of the response. Second, we estimate a per-voxel fiber response, which ...

The human brain forms a complex neural network with a connectional architecture that is still far from being known in full detail, even at the macroscopic level. The advent of diffusion MR imaging has enabled the exploration of the structural properties of white matter in vivo. In this article we propose a new forward model that maps the microscopic geometry of nervous tissue onto the water dif...

In analyzing diffusion magnetic resonance imaging, multi-tensor models address the limitations of the single diffusion tensor in situations of partial voluming and fiber crossings. However, selection of a suitable number of fibers and numerical difficulties in model fitting have limited their practical use. This paper addresses both problems by making spherical deconvolution part of the fitting...

Brain tissue types resolved using spherical deconvolution of multi-shell diffusion MRI data Ben Jeurissen, Jacques-Donald Tournier, Thijs Dhollander, Alan Connelly, and Jan Sijbers iMinds-Vision Lab, University of Antwerp, Antwerp, Belgium, The Florey Institute of Neuroscience and Mental Health, Melbourne, Victoria, Australia, Division of Imaging Sciences & Biomedical Engineering, King's Colleg...

We propose a new regularization for spherical deconvolution in diffusion MRI. It is based on observing that higher-order tensor representations of fiber ODFs should be H-psd, i.e., they should have a positive semidefinite (psd) matrix HT . We show that this constraint is stricter than the currently more widely used non-negativity, and that it can be enforced easily using quadratic cone programm...