Compressed Sensing via Measurement-Conditional Generative Models

A pre-trained generator has been frequently adopted in compressed sensing (CS) due to its ability to effectively estimate signals with the prior of NNs. In order to further refine the NN-based prior, we propose a framework that allows the generator to learn measurement-specific prior distribution, yielding more accurate prediction on a measurement. Our framework has a simple form that only utilizes additional information from a given measurement for prior learning, so it can be easily applied to existing methods. Despite its simplicity, we demonstrate through extensive experiments that our framework exhibits uniformly superior performances by large margin and can reduce the reconstruction error up to an order of magnitude for some applications. We also explain the experimental success in theory by showing that our framework can slightly relax the stringent signal presence condition, which is required to guarantee the success of signal recovery.