CoCPF: Coordinate-based Continuous Projection Field for Ill-Posed Inverse Problem in Imaging

Sparse-view computed tomography (SVCT) reconstruction aims to acquire CT images based on sparsely-sampled measurements. It allows the subjects exposed to less ionizing radiation, reducing the lifetime risk of developing cancers. Recent researches employ implicit neural representation (INR) techniques to reconstruct CT images from a single SV sinogram. However, due to ill-posedness, these INR-based methods may leave considerable ``holes'' (i.e., unmodeled spaces) in their fields, leading to sub-optimal results. In this paper, we propose the Coordinate-based Continuous Projection Field (CoCPF), which aims to build hole-free representation fields for SVCT reconstruction, achieving better reconstruction quality. Specifically, to fill the holes, CoCPF first employs the stripe-based volume sampling module to broaden the sampling regions of Radon transformation from rays (1D space) to stripes (2D space), which can well cover the internal regions between SV projections. Then, by feeding the sampling regions into the proposed differentiable rendering modules, the holes can be jointly optimized during training, reducing the ill-posed levels. As a result, CoCPF can accurately estimate the internal measurements between SV projections (i.e., DV sinograms), producing high-quality CT images after re-projection. Extensive experiments on simulated and real projection datasets demonstrate that CoCPF outperforms state-of-the-art methods for 2D and 3D SVCT reconstructions under various projection numbers and geometries, yielding fine-grained details and fewer artifacts. Our code will be publicly available.