Factorization with Missing and Noisy Data

Abstract. Several factorization techniques have been proposed for tack-ling the Structure from Motion problem. Most of them provide a good solution, while the amount of missing data is within an acceptable ra-tio. Focussing on this problem, we propose an incremental multiresolu-tion scheme able to deal with a high rate of missing data, as well as noisy data. It is based on an iterative approach that applies a classical factorization technique in an incrementally reduced space. Information recovered following a coarse-to-fine strategy is used for both, filling in the missing entries of the input matrix and denoising original data. A statistical study of the proposed scheme compared to a classical factor-ization technique is given. Experimental results obtained with synthetic data and real video sequences are presented to demonstrate the viability of the proposed approach.1