Compressive Sensing with Augmented Measurements via Generative Self-Distillation

Signal reconstruction from compressed, noisy observations is a ubiquitous challenge in various applications. To address its ill-posed nature, a suitable prior of the underlying signal is required. Generative adversarial networks (GANs) emerge as a natural prior, enabling realistic reconstructions. However, existing approaches either optimize a GAN conditioned on the measurements from scratch or use pre-trained GANs to find images that best fit real measurements. We propose an alternative GAN-based method that, instead of sampling directly from the signal distribution, generates low-dimensional synthetic observations from the real ones. An adversarial self-distillation strategy optimizes the GAN, extracting meaningful signal information for synthetic measurement generation. These samples form an augmented measurement set, improving the conditioning of compressed sensing solvers, including model-based and deep learning-based methods. We validate our approach on MNIST with a binary sensing matrix for the single-pixel camera, achieving significant improvements in ADMM, PnP-ADMM, and Unrolled ADMM using generated measurements.