Inverse of Affine Radon Transform for Light Field Reconstruction From Focal Stack

The light field can be applied to computational imaging methods, such as digital refocusing, depth reconstruction, and all-in-focus imaging. In this paper, the affine Radon transform of generating the focal stack by the light field is proposed. Then, we derive the inverse formula of the affine Radon transform for reconstructing the light field from the focal stack. We analyze the ill-posedness of the reconstruction problem by the inversion formula and the incompleteness of the focal stack data. The inversion formula reveals the instability of the solution. The focal stack can be regarded as the incomplete data for light field reconstruction in the spatial domain, while it corresponds to the limited support of light field in the Fourier domain. The numerical solution of light field reconstruction is realized by approximating the inverse of the affine Radon transform. Based on the approximated inverse affine Radon transform of light field reconstruction, the high-precision light field data reconstruction method and the computational imaging method can be established via the focal stack data. The experimental results show that the high-precision light field can be reconstructed from focal stack based on the approximated inverse affine Radon transform.