A Convex Approach to Low Rank Matrix Approximation with Missing Data

Many computer vision problems can be formulated as low rank bilinear minimization problems. One reason for the success of these problem is that they can be efficiently solved using singular value decomposition. However this approach fails if the measurement matrix contains missing data. In this paper we propose a new method for estimating missing data. Our approach is similar to that of L-1 approximation schemes that have been successfully used for recovering sparse solutions of under-determined linear systems. We use the nuclear norm to formulate a convex approximation of the missing data problem. The method has been tested on real and synthetic images with promising results.