A novel face-hallucination scheme based on singular value decomposition

• A method for estimating HR face images based on SVD is proposed.
• The singular values of an image at different resolutions have approximately linear relationships.
• Methods to estimate the singular values and the two matrices of a HR face are proposed.
• Our algorithm can produce plausible HR images from LR face images.

In this paper, an efficient mapping model based on singular value decomposition (SVD) is proposed for face hallucination. We can observe and prove that the main singular values of an image at one resolution have approximately linear relationships with their counterparts at other resolutions. This makes the estimation of the singular values of the corresponding high-resolution (HR) face images from a low-resolution (LR) face image more reliable. From the signal-processing point of view, this can effectively preserve and reconstruct the dominant information in the HR face images. Interpolating the other two matrices obtained from the SVD of the LR image does not change either the primary facial structure or the pattern of the face image. The corresponding two matrices for the HR face images can be constructed in a “coarse-to-fine” manner using global reconstruction. Our proposed method retains the holistic structure of face images, while the learned mapping matrices, which are represented as embedding coefficients of the individual mapping matrices learned from LR-HR training pairs, can be seen as holistic constraints in the reconstruction of HR images. Compared to state-of-the-art algorithms, experiments show that our proposed face-hallucination scheme is effective in terms of producing plausible HR images with both a holistic structure and high-frequency details.