| Abstract: |
| Bayesian statistical inversion and sparsity-based methods have long been effective mathematical tools for reducing sampling requirements in compressive sensing, enabling applications in underdetermined imaging systems such as MRI and CT. With the rapid advancement of deep learning, a new class of methods has emerged that learns data-driven representations, offering enhanced performance in signal and image reconstruction tasks. To address underdetermined and ill-conditioned inverse problems with limited measurements, we develop compressive sensing and Bayesian reconstruction frameworks that incorporate generative model-based priors. These approaches achieve improved reconstruction quality and computational efficiency compared to traditional regularization techniques and existing data-driven methods. Moreover, we establish theoretical guarantees for recovery performance under these generative priors. In this talk, I will present these methods and highlight recent results in applications including MRI reconstruction, phase retrieval, and other nonlinear inverse problems. |
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