Fourier feature network for 3D vessel reconstruction from biplane angiograms

3D reconstruction of biplane cerebral angiograms remains a challenging, unsolved research problem due to the loss of depth information and the unknown pixelwise correlation between input images. The occlusions arising from only two views complicate the reconstruction of fine vessel details and the simultaneous addressing of inherent missing information. In this paper, we take an incremental step toward solving this problem by reconstructing the corresponding 2D slice of the cerebral angiogram using biplane 1D image data. We developed a coordinate-based neural network that encodes the 1D image data along with a deterministic Fourier feature mapping from a given input point, resulting in a slice reconstruction that is more spatially accurate. Using only one 1D row of biplane image data, our Fourier feature network reconstructed the corresponding volume slices with a peak signal-to-noise ratio (PSNR) of 26.32 ± 0.36, a structural similarity index measure (SSIM) of 61.38 ± 1.79, a mean squared error (MSE) of 0.0023 ± 0.0002, and a mean absolute error (MAE) of 0.0364 ± 0.0029. Our research has implications for future work aimed at improving backprojection-based reconstruction by first examining individual slices from 1D information as a prerequisite.