Image Completion with Smooth Nonnegative Matrix Factorization

Abstract

Nonnegative matrix factorization is an unsupervised learning method for part-based feature extraction and dimensionality reduction of nonnegative data with a variety of models, algorithms, structures, and applications. Smooth nonnegative matrix factorization assumes the estimated latent factors are locally smooth, and the smoothness is enforced by the underlying model or the algorithm. In this study, we extended one of the algorithms for this kind of factorization to an image completion problem. It is the B-splines ADMM-NMF (Nonnegative Matrix Factorization with Alternating Direction Method of Multipliers) that enforces smooth feature vectors by assuming they are represented by a linear combination of smooth basis functions, i.e. B-splines. The numerical experiments performed on several incomplete images show that the proposed method outperforms the other algorithms in terms of the quality of recovered images.