Iterative Relaxed Collaborative Representation With Adaptive Weights Learning for Noise Robust Face Hallucination

In recent years, the collaborative representation (CR)-based techniques have been widely employed for face hallucination. However, the conventional CR model becomes less efficient in handling noisy low-resolution face images. In this paper, an iterative relaxed CR (iRCR) model with adaptive weights learning is presented to enhance the resolution of face images corrupted by noise. The core idea of iRCR is that a diagonal weight matrix is incorporated into the objective function, which helps to debase the influence of noise in representation. Different from existing collaborative methods with reweighting strategy where the weights require manually tuning, the weights in iRCR are adaptively learned to stay more consistent with the model error. Moreover, considering the local manifold structure property and nonlocal prior of small patches, the locality regularization and collaborative regularization are incorporated into a unified framework. This enables the proposed iRCR not only to capture the true topology structure of patch manifold but also to exploit the meaningful patterns among the whole training samples for reconstruction. Experimental results on both face dataset and real-world images demonstrate the superiority of our proposed method over several state-of-the-art face hallucination methods.