Rank-Regularized Measurement Operators for Compressive Imaging

Compressive imaging is used to acquire a small number of measurements of a scene, and perform effective reconstruction or high-level inference with purely data-driven models using deep learning. Although random projection has some advantages, we can get improved performance by learning the multiplexing patterns, also known as the measurement operator/matrix. However, at the time of training, it is not clear what the number of measurements should be. In this paper, we answer the following important question: How can we find the optimal number of measurements as well as the measurement matrix that can maintain a high-level of performance? Given the cost per measurement, our solution is to use regularization functions to encourage low-rank solutions for the learned measurement operator. We demonstrate that our solutions are effective on both image recognition and reconstruction problems.