Neural Network Learns Math Property for Low Coherence Sensing Matrices.

Compressive sensing is a powerful mathematical tool for perfectly recovering sparse signals, but its success heavily relies on the construction of an effective sensing matrix. Traditional methods for constructing these matrices often involve computationally challenging NP-hard problems related to properties like Restricted Isometry Property (RIP) or Null Space Property (NSP). For practical purposes, achieving low mutual coherence in the sensing matrix is key to perfect signal recovery. This research introduces a novel learning-based approach that uses a neural network to construct binary sensing matrices. What makes this technique unique is that it does not require any training dataset or specific application context. Instead, it directly incorporates a mathematical property—mutual coherence—into its loss function. This framework generates matrix entries through a shared underlying rule, resulting in a simple architecture that drastically reduces computational cost and storage requirements. This marks a significant advancement by using a mathematical property to define the loss function, offering a general and robust method for sensing matrix construction.