Matrix Completion using Block Toeplitz Matrix for Recovering an Incomplete Path-Tracing Image

Abstract

This paper introduces a novel matrix completion method to recover an incomplete path tracing image using a block Toeplitz matrix (BTM). The BTM provides an efficient numerical approach to create a low rank matrix from a single patch from an input image, which enables the recovery of missing pixels in the patch using matrix completion. Matrix completion is solved using weighted nuclear norm minimization with a parameter adjustment strategy. Previous approaches create a low rank matrix for matrix completion using similar patches across an image for every iteration of the optimization. Our method avoids this similar patch finding and the sophisticated initialization steps by using the BTM, improving the overall performance of matrix completion. We show efficient recovery of missing pixels of an incomplete path tracing image and partially damaged or occluded photograph.