Lipschitz Learning for Signal Recovery
This work addresses robust signal recovery for applications like compressive sensing, though it appears incremental as it builds on existing theoretical frameworks.
The authors tackled the problem of robust signal recovery from transformed observations using machine learning, establishing a Lipschitz condition that is necessary and sufficient for robust recovery and showing it is more general than the restricted isometry property in compressive sensing.
We consider the recovery of signals from their observations, which are samples of a transform of the signals rather than the signals themselves, by using machine learning (ML). We will develop a theoretical framework to characterize the signals that can be robustly recovered from their observations by an ML algorithm, and establish a Lipschitz condition on signals and observations that is both necessary and sufficient for the existence of a robust recovery. We will compare the Lipschitz condition with the well-known restricted isometry property of the sparse recovery of compressive sensing, and show the former is more general and less restrictive. For linear observations, our work also suggests an ML method in which the output space is reduced to the lowest possible dimension.