Depth Reconstruction of Multiple Light Sources Based on Compressed Sensing

Classical imaging system projects the surface of a 3-D object onto a 2-D sensor. The surface occupies only a small part of the observed volume. Therefore, the samples representing the volume form a sparse signal. We exploit this property in reconstruction of the scene depth from one severely defocused image. We propose a compressed sensing method for the reconstruction of scene in which the observed object consists of multiple light sources. For such an object, we discuss a model of optical system whose measurement matrix collects information that is sufficient for a unique reconstruction. Furthermore, we present the reconstruction of a scene from image divided into smaller parts which can be processed independently thus reducing computational complexity. We demonstrate successful reconstruction using simulated experiments, in which the objects consist of point light sources with white and with randomly distributed luminous intensities.