Focal stacks (FS) have attracted attention as an alternative representation of light field (LF). However, the problem of reconstructing LF from its FS is considered ill-posed. Although many regularization methods have been discussed, no method has been proposed to solve this problem perfectly. This paper showed that the LF can be perfectly reconstructed from the FS through a filter bank in theory for Lambertian scenes without occlusion if the camera aperture for acquiring the FS is a Cauchy function. The numerical simulation demonstrated that the filter bank allows perfect reconstruction of the LF.

A light field (LF), which is represented as a set of dense, multi-view images, has been used in various 3D applications. To make LF acquisition more efficient, researchers have investigated compressive sensing methods by incorporating certain coding functionalities into a camera. In this paper, we focus on a challenging case called snapshot compressive LF imaging, in which an entire LF is reconstructed from only a single acquired image. To embed a large amount of LF information in a single image, we consider two promising methods based on rapid optical control during a single exposure: time-multiplexed coded aperture (TMCA) and coded focal stack (CFS), which were proposed individually in previous works. Both TMCA and CFS can be interpreted in a unified manner as extensions of the coded aperture (CA) and focal stack (FS) methods, respectively. By developing a unified algorithm pipeline for TMCA and CFS, based on deep neural networks, we evaluated their performance with respect to other possible imaging methods. We found that both TMCA and CFS can achieve better reconstruction quality than the other snapshot methods, and they also perform reasonably well compared to methods using multiple acquired images. To our knowledge, we are the first to present an overall discussion of TMCA and CFS and to compare and validate their effectiveness in the context of compressive LF imaging.

A pupil function of aperture in image capturing systems is theoretically derived such that one can perfectly reconstruct all-in-focus image through linear filtering of the focal stack. The perfect reconstruction filters are also designed based on the derived pupil function. The designed filters are space-invariant; hence the presented method does not require region segmentation. Simulation results using synthetic scenes shows effectiveness of the derived pupil function and the filters.