Abstract: A method for denoising magnetic resonance images and data is disclosed herein. An example method includes receiving a series of MRF images from a scanning device; identifying one or more subsets of voxels for the series of MRF images; generating one or more sets of eigenvectors, each set of the one or more sets of eigenvectors corresponding to one of the one or more subsets of voxels, and each eigenvector of the one or more sets of eigenvectors having a corresponding eigenvalue; applying a noise distribution model to each of the eigenvalues; identifying a subset of the eigenvalues as corresponding to noise based on the noise distribution model; and reconstructing the series of MRF images without the subset of eigenvalues identified as corresponding to noise.

Abstract: Methods and systems for identifying and classifying multilinear data sets into a plurality of classes using invariant theory are disclosed herein. An example method includes receiving an input data set; computing a change of coordinates for each mode of the plurality of modes for the input data set using an invariant theory optimization algorithm by (i) constructing a chosen group and (ii) determining a group element in the chosen group; transforming the input data set into a relocated data set by applying each change of coordinates for each respective mode of the plurality of modes for the input data set by multiplying the subset of the input data set for each mode by the at least one matrix corresponding to each respective mode; and classifying, based on distances between coordinates in the relocated data set, the input data set into the plurality of classes.

Abstract: Techniques for predicting drug and target interactions in incomplete matrices are provided for use in new drug discovery and drug repurposing. Matrix completion is achieved through matrix factorization that employs coupled matrix-matrix completion processes capable of completing a drug-target interaction matrix using coupled input matrices of each dataset. Matrix completion techniques also extend to using coupled tensors containing multiple slices of each dataset and using coupled tensor-matrix completion techniques for predicting drug and target interactions.

Abstract: Techniques develop models for classification for physical conditions of a subject based on monitored physiologic signal data. The models for classification are determined from data transformed and feature extracted using a Taut-string transformation and in some instances using a further Stockwell-transformation, applied in parallel or in series. Physical conditions, specifying the state of hemodynamic stability and reflective of the cardiovascular and nervous systems, are thus modeled using these techniques.

Abstract: Techniques develop models for classification for physical conditions of a subject based on monitored physiologic signal data. The models for classification are determined from data transformed and feature extracted using a Taut-string transformation and in some instances using a further Stockwell-transformation, applied in parallel or in series. Physical conditions, specifying the state of hemodynamic stability and reflective of the cardiovascular and nervous systems, are thus modeled using these techniques.