Iterative Reconstruction Based on Latent Diffusion Model for Sparse Data Reconstruction

Reconstructing Computed tomography (CT) images from sparse measurement is a well-known ill-posed inverse problem. The Iterative Reconstruction (IR) algorithm is a solution to inverse problems. However, recent IR methods require paired data and the approximation of the inverse projection matrix. To address those problems, we present Latent Diffusion Iterative Reconstruction (LDIR), a pioneering zero-shot method that extends IR with a pre-trained Latent Diffusion Model (LDM) as a accurate and efficient data prior. By approximating the prior distribution with an unconditional latent diffusion model, LDIR is the first method to successfully integrate iterative reconstruction and LDM in an unsupervised manner. LDIR makes the reconstruction of high-resolution images more efficient. Moreover, LDIR utilizes the gradient from the data-fidelity term to guide the sampling process of the LDM, therefore, LDIR does not need the approximation of the inverse projection matrix and can solve various CT reconstruction tasks with a single model. Additionally, for enhancing the sample consistency of the reconstruction, we introduce a novel approach that uses historical gradient information to guide the gradient. Our experiments on extremely sparse CT data reconstruction tasks show that LDIR outperforms other state-of-the-art unsupervised and even exceeds supervised methods, establishing it as a leading technique in terms of both quantity and quality. Furthermore, LDIR also achieves competitive performance on nature image tasks. It is worth noting that LDIR also exhibits significantly faster execution times and lower memory consumption compared to methods with similar network settings. Our code will be publicly available.