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