Compressed Sensing MRI using Score-based Implicit Model

Abstract

In this thesis we study a newly emerged family of generative models; diffusion-based models, and propose a new method for solving inverse problems with significantly reduced computational cost. During the last three years, generative diffusion models constitute an important pole of interest for research that focuses on data generation and have contributed in the rapid evolution of domains among which are image generation (text-guided or not), shape and music generation. These models have achieved state-of-the-art performance regarding image synthesis quality, even beating GANs. In addition, multiple research works have utilized the generative capabilities of diffusion models to approach preexisting problems and have produced results that undermine previous techniques. More specifically, score-based models have been incorporated in a unified framework that approaches linear inverse problems, but suffers from high computational cost that prohibits its real-world deployment. In this thesis, we employ the equivalence between diffusion and score-based models and propose Score-based Implicit Model (SBIM) algorithm. SBIM is a reparameterization of DDIM algorithm - which uses diffusion models by default to produce samples - to incorporate score-based models. This way, we take advantage of DDIM's innate speed in order to extend the score-based framework by proposing an algorithm with significantly lower computational cost. In this work, we demonstrate the mathematical derivation of SBIM and successfully apply it to perform Compressed Sensing in MRI. The results, based on SSIM, PSNR and time evaluation metrics, confirm that SBIM can compete against previous methods and comprises a new tactic for accelerating inverse problem solutions using diffusion models.