Pseudoinverse Diffusion Models for Generative CT Image Reconstruction from Low Dose Data

Score-based diffusion models have significantly advanced generative deep learning for image processing. Measurement conditioned models have also been applied to inverse problems such as CT reconstruction. However, the conventional approach, culminating in white noise, often requires a high number of reverse process update steps and score function evaluations. To address this limitation, we propose an alternative forward process in score-based diffusion models that aligns with the noise characteristics of low-dose CT reconstructions, rather than converging to white noise. This method significantly reduces the number of required score function evaluations, enhancing efficiency and maintaining familiar noise textures for radiologists, Our approach not only accelerates the generative process but also retains CT noise correlations, a key aspect often criticized by clinicians for deep learning reconstructions. In this work, we rigorously define a matrix-controlled stochastic process for this purpose and validate it through computational experiments. Using a dataset from The Cancer Genome Atlas Liver Hepatocellular Carcinoma (TCGA-LIHC), we simulate low-dose CT measurements and train our model, comparing it with a baseline scalar diffusion process and conditional diffusion model. Our results demonstrate the superiority of our pseudoinverse diffusion model in terms of efficiency and the ability to produce high-quality reconstructions that are familiar in texture to medical professionals in a low number of score function evaluations. This advancement paves the way for more efficient and clinically practical diffusion models in medical imaging, particularly beneficial in scenarios demanding rapid reconstructions or lower radiation exposure.