Compressed sensing using generative models : theory and applications




Jalal, Ajil

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Deep generative models, such as Generative Adversarial Networks, Variational Autoencoders, Flow-based models, and Score-based models, have shown excellent performance in modelling high-dimensional distributions. This dissertation proposes a novel framework that can leverage the power of these models for solving various problems in signal processing, such as compressed sensing, inpainting, and super-resolution, to name a few. On the theoretical side, we propose algorithms that provably achieve optimal sample complexities and are also robust to different kinds of corruptions. On the practical side, we show that our algorithms can provide performance improvements over classical algorithms such as the LASSO. Furthermore, our most recent work shows that our approach achieves state-of-the art performance on real-world MRI reconstruction tasks.


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