Processing multidimensional signals

#The following relates generally to signal processing, and more particularly to a computer-implemented method, a computing system, and a computer program product for processing multidimensional signals captured from physical space.

#Raw multidimensional signals may be captured from physical space by various devices, using various techniques, and for various uses. In the field of data processing, it is often a goal to process raw multidimensional signals in order to obtain representations of the signals that are more useful than when in raw form, for subsequent processing and other operations such as classification, visualization and the like.

#Various techniques for processing multidimensional signals in an attempt to obtain more useful representations through reconstruction, for example by way of dimensionality reduction, include the well-understood principle component analysis (PCA) and multidimensional scaling (MDS) techniques. Each of PCA and MDS are eigenvector techniques that are useful for modeling linear variabilities in raw multidimensional data.

#Embodiments of the invention will now be described with reference to the appended drawings in which:

#FIG. 1A is a graphical depiction of a voxel modelled as a black body in a three-dimensional Cartesian physical space, along with spatially neighbouring voxels;

#FIG. 1B is a plot of the relative fMRI BOLD signal intensities of spatially neighbouring points relative to the origin representing the black body relative to its spatial neighbours;

#The description of the invention to follow is, for ease of understanding, made in connection with an embodiment where the dataset of multidimensional signals is a dataset of functional Magnetic Resonance Imaging (fMRI) BOLD (Blood Oxygenation Level Dependent) signals. However, it will be understood that the invention is applicable to the processing of datasets of other kinds of multidimensional signals captured from points in a physical space, such as other spatiotemporal signals, of which fMRI BOLD signals are an example.

#A local interpretation of fMRI data may be expressed in terms of a BOLD signal comprising BOLD intensity values over T time points (T being greater than or equal to 1) being a T-dimensional spatial pattern observed at the spatial point in the physical space being assessed, as defined by the respective point of the voxel in the fMRI data.

#A global interpretation of fMRI data may be expressed in terms of the fMRI data containing T uniformly-spaced time points, where time point tε{1, . . . , T} references a physical space that is a three-dimensional volume comprised of V=L×W×H points, or voxels (volumetric elements), having a respective BOLD intensity value. That is, each voxel is a volumetric measurement of the brain's physical mechanisms in both space and time. The measurement may be expressed as four-tuple (x, y, z, t).