Magnetic Resonance Imaging (MRI) is a critical tool in medical diagnosis and treatment planning due to its excellent soft tissue contrast and non-ionizing nature. However, MRI faces challenges like prolonged scan times and data acquisition constraints arising from patient privacy concerns and heterogeneous medical data. This thesis introduces computationally efficient deep learning algorithms to address these challenges in two parts.In Part I, we focus on MRI reconstruction under limited or no data availability. For limited data, we propose the LONDN MRI method, which trains on a small set of adaptively chosen neighboring images, achieving superior performance compared to supervised models like MoDL, with significant improvement. For data-free scenarios, we develop Self-Guided DIP and Autoencoding Sequential DIP (aSeqDIP), which leverage self-regularization and sequential U-Net architectures to improve both performance and efficiency, outperforming traditional supervised models. In Part II, we enhance the robustness and generalization capabilities of medical imaging models using a combination of randomized smoothing and diffusion-based purification. We introduce SMUG, an unrolling method that mitigates worst-case perturbations and data variations such as mask shifts and noise. Additionally, our Diffusion Purification framework effectively removes noise in biomedical lesion data, surpassing adversarial training and other robustness methods. These contributions advance MRI reconstruction and robust medical imaging, addressing critical limitations in clinical workflows.
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