  We propose Coordinate-based Internal Learning (CoIL) as a new deep-learning
(DL) methodology for the continuous representation of measurements. Unlike
traditional DL methods that learn a mapping from the measurements to the
desired image, CoIL trains a multilayer perceptron (MLP) to encode the complete
measurement field by mapping the coordinates of the measurements to their
responses. CoIL is a self-supervised method that requires no training examples
besides the measurements of the test object itself. Once the MLP is trained,
CoIL generates new measurements that can be used within a majority of image
reconstruction methods. We validate CoIL on sparse-view computed tomography
using several widely-used reconstruction methods, including purely model-based
methods and those based on DL. Our results demonstrate the ability of CoIL to
consistently improve the performance of all the considered methods by providing
high-fidelity measurement fields.
