Sensing Theorems for Unsupervised Learning in Linear Inverse Problems

Solving an ill-posed linear inverse problem requires knowledge about the underlying signal model. In many applications, this model is a priori unknown and has to be learned from data. However, it is impossible to learn the model using observations obtained via a single incomplete measurement operator, as there is no information about the signal model in the nullspace of the operator, resulting in a chicken-and-egg problem: to learn the model we need reconstructed signals, but to reconstruct the signals we …

applications chicken data information knowledge learn linear measurement sensing signal unsupervised unsupervised learning