Tutorial abstract

Summary form only given, as follows. The goal of this tutorial is to provide the ICIG community with an introduction to the quickly developing area of low-rank matrix recovery. Low-rank (or approximately low-rank) matrices arise in a great number of applications involving image and video data. A few recurrent examples in this tutorial will include aligning batches of images, super-resolution and video inpainting, and in background modeling for visual tracking and surveillance. However, in real applications our observations are never prefect: observations are always noisy, often missing, and sometimes grossly or even maliciously corrupted. The recent excitement surrounding low-rank matrix recovery is due to very recent results showing that under fairly general circumstances, the low rank recovery problem can be efficiently and exactly solved, by convex programming. These theoretical advances have inspired a flurry of algorithmic work, giving increasingly practical and scalable algorithms for solving the corresponding convex programs. The theory and algorithms described above, which the proposers have had a strong role in developing, are already beginning to influence practice in a number of areas, including collaborative filtering and computer vision. However, we believe these results are poised for even stronger impact in image processing. The purpose of this tutorial is to bring these ideas to the ICIG community, by giving a solid and unified introduction to the existing theoretical and algorithmic state of the art in the area, and then show how this theory and algorithms are already being used to solve real imaging problems.