Processing multidimensional signal

Abstract

A computer-implemented method, computing system and non-transitory computer readable medium having computer readable code thereon for processing a dataset of multidimensional signals captured from points in a physical space. The computer-implemented method includes using a computing system, determining, for each of the points, a plurality of spatially neighboring points in the physical space; and using the computing system, creating a modified signal for each point based on the signals of its respective spatially neighboring points

1 . A method of processing multidimensional signals representing an object, comprising:
 receiving the multidimensional signals representing a plurality of separated nonlinear manifolds captured by at least one detector from the object, represented as a plurality of elements in an array;   constructing a modified array of elements having reconstruction errors of the separated nonlinear manifolds on the same scale, using at least one automated processor; and   presenting a reconstructed representation of the object, based on the modified array of elements, using the at least one automated processor.   
     
     
         2 . The method according to  claim 1 , wherein said constructing comprises:
 determining distances to spatial neighbors of the plurality of elements in the array;   linearizing spatial indices in the array to produce a linearized array of elements, constrained to maintain spatial neighbor relationships of the plurality of elements in the array, using at least one automated processor; and   generating reconstruction weights for reconstructing the linearized array of elements, using locally linear embedding, at a minimized cost of reconstruction, based on at least distances of the spatial neighbors from the respective element, using the at least one automated processor.   
     
     
         3 . The method according to  claim 1 , wherein the modified array of elements is defined in a Lebesgue space, and has unit covariance. 
     
     
         4 . The method according to  claim 1 , wherein the representation comprises a set of voxels of the object, each voxel modelled as a black body in a three-dimensional Cartesian physical space. 
     
     
         5 . The method according to  claim 4 , wherein each voxel represents magnetic resonance image data. 
     
     
         6 . The method according to  claim 1 , further comprising storing, in association with each element, coordinates of the spatial neighbors in an order corresponding to their respective determined distances from the respective element. 
     
     
         7 . The method according to  claim 1 , further comprising computing a respective covariance between the multidimensional signals of each spatial neighbor, less the multidimensional signal of the element, and the multidimensional signal of the element, wherein the reconstruction weights for each spatially neighbor are generated based on a constrained local least-squares optimization of the covariances. 
     
     
         8 . The method according to  claim 1 , wherein the spatial neighbors of each element comprise elements within a spherical subvolume centered at the element having a predetermined radius. 
     
     
         9 . The method according to  claim 1 , wherein the objects are three-dimensional objects. 
     
     
         10 . A system for processing multidimensional signals, comprising:
 an array representing a plurality of elements stored in a memory, comprising multidimensional signals representing a plurality of separated nonlinear manifolds captured by at least one detector from the object;   at least one automated processor configured to construct a modified array of elements representing origin-centered manifolds in both space and time having unit covariance; and   an output port presenting a reconstructed representation of the object, based on the modified array of elements, using the at least one automated processor.   
     
     
         11 . The system according to  claim 10 , wherein the at least one automated processor is further configured to:
 linearize spatial indices of the array to produce a linearized array of elements, constrained to maintain a spatial neighbor relationship with the spatial neighbors of the plurality of elements determined based on distances between respective elements;   generate reconstruction weights for each respective element of the linearized array of elements, for reconstructing the linearized array of elements at a minimized cost of reconstruction based on the spatial neighbors of each respective element, using locally linear embedding; and   construct a modified array of elements based on the generated reconstruction weights.   
     
     
         12 . The system according to  claim 11 , wherein the at least one automated processor is further configured to compute a respective covariance between the multidimensional signals of each spatial neighbor less the multidimensional signal of the element, and the multidimensional signal of the element, wherein the reconstruction weights for each spatially neighbor are generated based on a constrained local least-squares optimization of the covariances. 
     
     
         13 . The system according to  claim 11 , wherein the array is in a Lebesgue space, and the modified array of elements has unit covariance. 
     
     
         14 . The system according to  claim 10 , wherein the representation comprises a set of voxels of the object, each voxel modelled as a black body in a three-dimensional Cartesian physical space. 
     
     
         15 . The system according to  claim 14 , wherein the multidimensional signals represent magnetic resonance image data. 
     
     
         16 . The system according to  claim 15 , wherein the magnetic resonance image data comprises functional Magnetic Resonance Imaging (fMRI) BOLD (Blood Oxygenation Level Dependent) signals. 
     
     
         17 . The system according to  claim 10 , wherein the objects are three-dimensional objects and the linearized array of elements is at least three dimensional. 
     
     
         18 . A method of generating a modified representation of medical imaging signals representing volumetric elements modelled as black bodies in a physical space, comprising:
 receiving an array of medical imaging signals as an input dataset;   determining distances between volumetric elements within the array;   determining spatial neighbors of the volumetric elements in the array based on the determined distances;   linearizing spatial indices of the array to produce a linearized array constrained to maintain a spatial neighbor relationship with the determined spatial neighbors of the volumetric elements, defining a Lebesgue space;   generating reconstruction weights for reconstructing the linearized array, using locally linear embedding, at a minimized cost of reconstruction from the spatial neighbors;   constructing a modified array of volumetric elements using a constrained global least squares optimization based on the reconstruction weights, wherein the volumetric elements of the modified array have unit covariance; and   presenting a medical image, based on the modified array of volumetric elements.   
     
     
         19 . The method according to  claim 18 , wherein the medical image signals comprise a set of voxels of the object representing magnetic resonance image data over time, each voxel modelled as a black body in a three-dimensional Cartesian physical space over time. 
     
     
         20 . The method according to  claim 18 ,
 further comprising computing a respective covariance between the multidimensional signals of each spatial neighbor less the multidimensional signal of the element, and the multidimensional signal of the element,   wherein the reconstruction weights for each spatially neighbor are generated based on a constrained local least-squares optimization of the covariances, and   wherein the spatial neighbors of each element comprise elements within a spherical subvolume centered at the element having a predetermined radius.