Measure theoretic imaging, with an example employing magnetic resonance input

Abstract

We present a new medical imaging principle which allows reconstruction of images (from the output of a general digital imaging technology) whose contrast is based on a fundamentally different mathematical mechanism than that of standard images. These images have the useful property that they are capable of exhibiting high contrast between tissues which in currently produced images necessarily have low contrast. The meaning of these images, and their general place in the context of present image generation techniques, is most naturally expressed in the formalism of measure theory. The property actually imaged is derived from a probability measure associated with the mapping which expresses the output of the imaging technology. It also has a nonprobabilistic interpretation as a generalization of the Jacobian, specifically, the Radon-Nikodym derivative. In particular, unlike standard images, contrast is independent of the metric in the space of physical signals that the imaging technology associates with points of the region to be imaged. Images based on this approach using magnetic resonance input are presented.