Filtered back projection-deconvolution method for light field reconstruction from the focal stack

In the simplification, a light field is a four-dimensional (4D) function, and light field reconstruction aims to recover this 4D function from a three-dimensional (3D) focal stack, so it is a seriously ill-posed reconstruction problem from incomplete projection data. Based on the known 3D data of the focal stack in the frequency domain, we introduce a 3D assumption for the light field and derive an analytical reconstruction formula of the light field with an infinite depth range ρ. Subsequently, we establish the filtered back projection (FBP) algorithm to reconstruct the light field from the focal stack. Under certain assumptions concerning the light field and window functions, we prove the convergence of our proposed method at any continuous point. Since in actual data sampling scenarios, the light field is reconstructed only by a small number of focal stacks, a deconvolution algorithm is introduced based on the FBP algorithm to further enhance quality, which is called the filtered back projection-deconvolution (FBP-D) method. Our experimental results demonstrate the superiority of the proposed algorithm compared to the FBP method and other existing methods. Notably, the algorithm exhibits enhanced performance when employing a smooth boundary window and a larger depth range ρ.