Deep Compressed Sensing

Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is highly flexible and data efficient, but its application has been restricted by the strong assumption of sparsity and costly optimisation process. A recent approach that combines CS with neural network generators has removed the constraint of sparsity, but reconstruction remains slow. Here we propose a novel framework that significantly improves both the performance and speed of signal recovery by jointly training a generator and the optimisation process for reconstruction via meta-learning. We explore training the measurements with different objectives, and derive a family of models based on minimising measurement errors. We show that Generative Adversarial Nets (GANs) can be viewed as a special case in this family of models. Borrowing insights from the CS perspective, we develop a novel way of stabilising GAN training using gradient information from the discriminator.