Di-chromatic Interpolation of Magnetic Resonance Metabolic Imagery

Magnetic resonance imaging with hyperpolarized contrast agents can provide unprecedented \textit{in-vivo} measurements of metabolism, but yields images that are lower resolution than that achieved with proton anatomical imaging. In order to spatially localize the metabolic activity, the metabolic image must be interpolated to the size of the proton image. The most common methods for choosing the unknown values rely exclusively on values of the original un-interpolated image. In this work, we present an alternative method that uses the higher-resolution proton image to provide additional spatial structure. The interpolated image is the result of a convex optimization algorithm which is solved with the Fast Iterative Shrinkage Threshold Algorithm (FISTA). Results are shown with images of hyperpolarized pyruvate, lactate, and bicarbonate using data of the heart and brain from healthy human volunteers, a healthy porcine heart, and a human with prostate cancer.