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Most modern face super-resolution methods resort to convolutional neural networks (CNN) to infer high-resolution (HR) face images. When dealing with very low resolution (LR) images, the performance of these CNN based methods greatly degrades. Meanwhile, these methods tend to produce over-smoothed outputs and miss some textural details. To address these challenges, this paper presents a wavelet-based CNN approach that can ultra-resolve a very low resolution face image of 16x16 or smaller pixel-size to its larger version of multiple scaling factors (2x, 4x, 8x and even 16x) in a unified framework. Different from conventional CNN methods directly inferring HR images, our approach firstly learns to predict the LR's corresponding series of HR's wavelet coefficients before reconstructing HR images from them. To capture both global topology information and local texture details of human faces, we present a flexible and extensible convolutional neural network with three types of loss: wavelet prediction loss, texture loss and full-image loss. Extensive experiments demonstrate that the proposed approach achieves more appealing results both quantitatively and qualitatively than state-of-the-art super-resolution methods.