Wavelet-Inspired Multi-channel Score-based Model for Limited-angle CT Reconstruction

Score-based generative model (SGM) has demonstrated great potential in the challenging limited-angle CT (LA-CT) reconstruction. SGM essentially models the probability density of the ground truth data and generates reconstruction results by sampling from it. Nevertheless, direct application of the existing SGM methods to LA-CT suffers multiple limitations. Firstly, the directional distribution of the artifacts attributing to the missing angles is ignored. Secondly, the different distribution properties of the artifacts in different frequency components have not been fully explored. These drawbacks would inevitably degrade the estimation of the probability density and the reconstruction results. After an in-depth analysis of these factors, this paper proposes a Wavelet-Inspired Score-based Model (WISM) for LA-CT reconstruction. Specifically, besides training a typical SGM with the original images, the proposed method additionally performs the wavelet transform and models the probability density in each wavelet component with an extra SGM. The wavelet components preserve the spatial correspondence with the original image while performing frequency decomposition, thereby keeping the directional property of the artifacts for further analysis. On the other hand, different wavelet components possess more specific contents of the original image in different frequency ranges, simplifying the probability density modeling by decomposing the overall density into component-wise ones. The resulting two SGMs in the image-domain and wavelet-domain are integrated into a unified sampling process under the guidance of the observation data, jointly generating high-quality and consistent LA-CT reconstructions. The experimental evaluation on various datasets consistently verifies the superior performance of the proposed method over the competing method.