CoIL: Coordinate-based Internal Learning for Imaging Inverse Problems

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.