Image completion with nonnegative matrix factorization under separability assumption

Abstract

Nonnegative matrix factorization is a well-known unsupervised learning method for part-based feature extraction and dimensionality reduction of a nonnegative matrix with a variety of applications. One of them is a matrix completion problem in which missing entries in an observed matrix is recovered on the basis of partially known entries. In this study, we present a geometric approach to the low-rank image completion problem with separable nonnegative matrix factorization of an incomplete data. The proposed method recursively selects extreme rays of a simplicial cone spanned by an observed image and updates the latent factors with the hierarchical alternating least-squares algorithm. The numerical experiments performed on several images with missing entries demonstrate that the proposed method outperforms other algorithms in terms of computational time and accuracy.