Shift-Invariant-Subspace Discretization and Volume Reconstruction for Light Field Microscopy

Light Field Microscopy (LFM) is an imaging technique that captures 3D spatial information with a single 2D image. LFM is attractive because of its relatively simple implementation and fast volume acquisition rate. Capturing volume time series at a camera frame rate can enable the study of the behaviour of many biological systems. For instance, it could provide insights into the communication dynamics of living 3D neural networks. However, conventional 3D reconstruction algorithms for LFM typically suffer from high computational cost, low lateral resolution, and reconstruction artifacts. In this work, we study the origin of these issues and propose novel techniques to improve the performance of the reconstruction process. First, we propose a discretization approach that uses shift-invariant subspaces to generalize the typical discretization framework used in LFM. Then, we study the shift-invariant-subspace assumption as a prior for volume reconstruction under ideal conditions. Furthermore, we present a method to reduce the computational time of the forward model by using singular value decomposition (SVD). Finally, we propose to use iterative approaches that incorporate additional priors to perform artifact-free 3D reconstruction from real light field images. We experimentally show that our approach performs better than Richardson-Lucy-based strategies in computational time, image quality, and artifact reduction.