Sampling and Recovery of Binary Shapes via Low-Rank structures

The binary-valued images usually represent shapes. Therefore, the recovery of binary images from samples is often linked with recovery of shapes, where certain parametric structures are assumed on the shape. In this paper, we study the recovery of shape images with the perspective of low-rank matrix recovery. The matrix of such images is not automatically low-rank. Therefore, we consider the Hankel transformation of binary images in order to apply tools in low-rank matrix recovery. We introduce an ADMM technique for the reconstruction which is numerically confirmed to yield suitable results. We also analyze the sampling requirement of this process based on the theory of random matrices.