Non-stationary multi-output gaussian processes for enhancing resolution over diffusion tensor fields

Diffusion magnetic resonance imaging (dMRI) is an advanced technique derived from magnetic resonance imaging (MRI) that allows the study of internal structures in biological tissue. Due to acquisition protocols and hardware limitations of the equipment employed to obtain the data, the spatial resolution of the images is often low. This inherent lack in dMRI is a considerable difficulty because clinical applications are affected. The scientific community has proposed several methodologies for enhancing the spatial resolution of dMRI data, based on interpolation of diffusion tensors fields. However, most of the methods have considerable drawbacks when they interpolate strong transitions, such as crossing fibers. Also, relevant clinical information from tensor fields is modified when interpolation is performed. In this work, we propose a probabilistic methodology for interpolation of diffusion tensors fields using multi-output Gaussian processes with non-stationary kernel function. First, each tensor is decomposed in shape and orientation features. Then, the model interpolates the features jointly. Results show that proposed approach outperforms state-of-the-art methods regarding resolution enhancement accuracy on synthetic and real data, when we evaluate interpolation quality with Frobenius and Riemann metrics. Also, the proposed method demonstrates an adequate characterization of both stationary and non-stationary fields, contrary to previous approaches where performance is seriously reduced when complex fields are interpolated.