Locality preserving projections as a new manifold analysis approach for robust face super-resolution

Abstract

In this paper, we propose a novel method for performing robust super-resolution of face images by solving the practical problems of the traditional manifold analysis. Face super-resolution is to recover a high-resolution face image from a given low-resolution face image by modeling the face image space in view of multiple resolutions. In particular, face super-resolution is useful to enhance face images captured from surveillance footage. Face super-resolution should be preceded by analyzing the characteristics of the face image distribution. In literature, it has been shown that face images lie on a nonlinear manifold by various manifold learning algorithms, so if the manifold structure is taken into consideration for modeling the face image space, the results of face super-resolution can be improved. However, there are some practical problems which prevent the manifold analysis from being applied to super-resolution. Almost all of the manifold learning methods cannot generate mapping functions for new test images which are absent from a training set. Also, there exists another significant problem when applying the manifold analysis to super-resolution; superresolution seeks to recover a high-dimensional image from a low-dimensional one while manifold learning methods perform the exact opposite for dimensionality reduction. To break those limitations of applying the manifold analysis to super-resolution, we propose a novel face superresolution method using Locality Preserving Projections (LPP). LPP gives an advantage over other manifold learning methods in that it has well-defined linear projections which allow us to formulate well-defined mappings between highdimensional data and low-dimensional data. Moreover, we show that LPP coefficients of an unknown high-resolution image can be inferred from a given low-resolution image using a MAP estimator.