Abstract: A method for analysis of complex spatio-temporal data within a dynamic system that includes spatial positions and fields, at least a portion of which are interacting, includes determining values of mean field at every spatial position, determining spatio-temporal eigenmodes in spatial-frequency space assuming interacting fields, and determining spatial and temporal interactions between the eigenmodes. The resulting display indicates space/time localization patterns that are indicative of connectivity within the dynamic system.

Abstract: A method for registering multiple data types of diverse modalities for a target volume includes acquiring at least at least two datasets associated with the target volume where the at least two datasets having different modalities. Using information field theory and entropy spectrum pathways theory, a local connectivity matrix is constructed for one or both of spatial connectivity and temporal connectivity for each of the datasets. The local connectivity matrices for the datasets are fused into a common coupling matrix and the datasets are merged to generate a registered image displaying the spatial and temporal features within the target volume.

Abstract: A method and for estimating local diffusion anisotropy and global tractography within neural architecture from diffusion weighted magnetic resonance image (dMRI) data uses a computer processor to integrate a first dataset comprising standard single pulsed field gradient (sPFG) dMRI data with a second dataset comprising double pulsed field gradient (dPFG) dMRI data into a common coordinate system with the same spatial resolution. The resulting image includes integrated macroscopic and microscopic anisotropy and global tractography within the target volume.

Abstract: A method for analysis of complex spatio-temporal data within a dynamic system that includes spatial positions and fields, at least a portion of which are interacting, includes determining values of mean field at every spatial position, determining spatio-temporal eigenmodes in spatial-frequency space assuming interacting fields, and determining spatial and temporal interactions between the eigenmodes. The resulting display indicates space/time localization patterns that are indicative of connectivity within the dynamic system.

Abstract: A system and method for analysis of complex spatio-temporal data utilize complimentary general approaches to data analysis: information field theory (IFT), which reformulates Bayesian theory in terms of field theory in order to incorporate the important and often overlooked conditions that ensure continuity of underlying parameter spaces that are to be estimated from discrete data, and entropy spectrum pathways (ESP), which uses the principle of maximum entropy to incorporate prior information on the structure of the underlying space in order to estimate measures of connectivity.

Abstract: A method and for estimating local diffusion anisotropy and global tractography within neural architecture from diffusion weighted magnetic resonance image (dMRI) data uses a computer processor to integrate a first dataset comprising standard single pulsed field gradient (sPFG) dMRI data with a second dataset comprising double pulsed field gradient (dPFG) dMRI data into a common coordinate system with the same spatial resolution. The resulting image includes integrated macroscopic and microscopic anisotropy and global tractography within the target volume.

Abstract: A method and system for registration of a multi-dimensional image include defining an input image and a reference image in the same fixed Cartesian grid, then mapping locations within the reference image and the input image to phase space using a Hamiltonian function to define a symplectomorphic map, where the map is embedded in an energy shell. The mapping step is iterated until a sequence of energy shells is created. The energy shells are used generate curvilinear mapping grid which is then applied to the first image to generate a registered output image data. The data may be preconditioned to account for nearest neighbor coupling and/or to equalize the dimensionality of the images.

Abstract: A method and system for registration of a multi-dimensional image include defining an input image and a reference image in the same fixed Cartesian grid, then mapping locations within the reference image and the input image to phase space using a Hamiltonian function to define a symplectomorphic map, where the map is embedded in an energy shell. The mapping step is iterated until a sequence of energy shells is created. The energy shells are used generate curvilinear mapping grid which is then applied to the first image to generate a registered output image data. The data may be preconditioned to account for nearest neighbor coupling and/or to equalize the dimensionality of the images.

Abstract: A method for registering multiple data types of diverse modalities for a target volume includes acquiring at least at least two datasets associated with the target volume where the at least two datasets having different modalities. Using information field theory and entropy spectrum pathways theory, a local connectivity matrix is constructed for one or both of spatial connectivity and temporal connectivity for each of the datasets. The local connectivity matrices for the datasets are fused into a common coupling matrix and the datasets are merged to generate a registered image displaying the spatial and temporal features within the target volume.

Abstract: A method is provided for modeling complex shapes from volumetric data utilizing spherical wave decomposition (SWD) by combining angular-only basis functions of the SPHARM with radial basis functions obtained by asymptotic expansion as a series of sine and cosine Fourier transforms to form the complete 3D basis. The 3D basis is used to expand the volumetric data. The resulting 3D volume representation allows construction of images of both surface and internal structures of the target object.

Abstract: A system and method for analysis of complex spatio-temporal data utilize complimentary general approaches to data analysis: information field theory (IFT), which reformulates Bayesian theory in terms of field theory in order to incorporate the important and often overlooked conditions that ensure continuity of underlying parameter spaces that are to be estimated from discrete data, and entropy spectrum pathways (ESP), which uses the principle of maximum entropy to incorporate prior information on the structure of the underlying space in order to estimate measures of connectivity.

Abstract: A method for fiber tractography processes multi-shell diffusion weighted MRI data to identify fiber tracts by calculating intravoxel diffusion characteristics from the MRI data. A transition probability is calculated for each possible path on the lattice, with the transition probability weighted according the intravoxel characteristics. Entropy is calculated for each path and the paths are ranked according to entropy. A geometrical optics algorithm is applied to the entropy data to define pathways, which are ranked according to their significance to generate a map of the pathways.

Abstract: A method for modeling complex shapes from volumetric data utilizing spherical wave decomposition (SWD) combines angular-only basis functions of the SPHARM with spherical Bessel functions as the radial basis functions to form the complete 3D basis. The 3D basis is then used to expand the volumetric data. The resulting 3D volume representation allows images to be generated of both surface and internal structures of the target object.

Abstract: A method for fiber tractography processes multi-shell diffusion weighted MRI data to identify fiber tracts by calculating intravoxel diffusion characteristics from the MRI data. A transition probability is calculated for each possible path on the lattice, with the transition probability weighted according the intravoxel characteristics. Entropy is calculated for each path and the paths are ranked according to entropy. A geometrical optics algorithm is applied to the entropy data to define pathways, which are ranked according to their significance to generate a map of the pathways.

Abstract: A new transform is disclosed, applying methods of group theory, with which the composition of a voxel of three channels comprising isotropic, single fiber and multiple fiber components can be determined, as well as the magnitude and orientation of the diffusion field. Asymmetries produced by experimental artifacts fall into channels distinct from the fiber channels, allowing their separation and a subsequent reduction in noise from the reconstructed fibers.

Abstract: A noninvasive method using nuclear magnetic resonance (NMR) to simultaneously obtain quantitative information and accurate imaging of structures and flow of a subject. The method is particularly suited to the study of anatomical detail and blood flow within the human body. Flow induces phase shifts are distinguished from systematic phases produced during image formation, thereby enabling the separation of flowing and stationary components.