Robust Image Reconstruction from Multiview Measurements
We propose a novel method to accurately reconstruct a set of images representing a single scene from a few linear multiview measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background image is common to all observed images but undergoes geometric transformations, as the scene is observed from different viewpoints. In this paper, we assume that these geometric transformations are represented by a few parameters, e. g., translation, rotation, affine transformation, etc.. The foreground images differ from one observed image to another, and are used to model possible occlusions of the scene. The proposed reconstruction algorithm estimates jointly the images and the transformation parameters from the available multiview measurements. The ideal solution of this multiview imaging problem minimizes a nonconvex functional, and the reconstruction technique is an alternating descent method built to minimize this functional. The convergence of the proposed algorithm is studied, and conditions under which the sequence of estimated images and parameters converges to a critical point of the nonconvex functional are provided. Finally, the efficiency of the algorithm is demonstrated using numerical simulations for applications such as compressed sensing or superresolution.