Face hallucination technologies have been widely developed during the past decades, among which the sparse manifold learning (SML)-based approaches have become the popular ones and achieved promising performance. However, these SML methods always failed in handling noisy images due to the least-square regression (LSR) they used for error approximation. To this end, we propose, in this article, a smooth correntropy representation (SCR) model for noisy face hallucination. In SCR, the correntropy regularization and smooth constraint are combined into one unified framework to improve the resolution of noisy face images. Specifically, we introduce the correntropy induced metric (CIM) rather than the LSR to regularize the encoding errors, which admits the proposed method robust to noise with uncertain distributions. Besides, the fused LASSO penalty is added into the feature space to ensure similar training samples holding similar representation coefficients. This encourages the SCR not only robust to noise but also can well exploit the inherent typological structure of patch manifold, resulting in more accurate representations in noise environment. Comparison experiments against several state-of-the-art methods demonstrate the superiority of SCR in super-resolving noisy low-resolution (LR) face images.

中文翻译：

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基于平滑熵表示的噪声鲁棒幻脸


人脸幻觉技术在过去几十年中得到了广泛的发展，其中基于稀疏流形学习（SML）的方法已成为流行的方法并取得了可喜的性能。然而，由于使用最小二乘回归（LSR）进行误差近似，这些 SML 方法在处理噪声图像时总是失败。为此，我们在本文中提出了一种用于噪声面部幻觉的平滑相关熵表示（SCR）模型。在SCR中，将相关熵正则化和平滑约束结合到一个统一的框架中，以提高噪声人脸图像的分辨率。具体来说，我们引入了相关熵诱导度量（CIM）而不是LSR来规范编码错误，这使得所提出的方法对不确定分布的噪声具有鲁棒性。此外，将融合的LASSO惩罚添加到特征空间中，以确保相似的训练样本具有相似的表示系数。这使得 SCR 不仅对噪声具有鲁棒性，而且可以很好地利用贴片流形的固有类型结构，从而在噪声环境中获得更准确的表示。与几种最先进方法的比较实验证明了 SCR 在超分辨率噪声低分辨率 (LR) 人脸图像中的优越性。