Heteroskedasticity tuned mixed-norm sparse regularization for face hallucination

Face hallucination is typically an ill-posed inverse problem, so it is essential to exploit an effective norm-regularized underlying representation. Due to the under-sparsity or over-sparsity, the widely used regularization methods, such as ridge regression and sparse representation, lead to poor robustness in the presence of noise. In addition, standard forms of penalty functions fail to account for the nature of heteroskedasticity of reconstruction coefficients, thus hardly providing optimal solutions in terms of accuracy and stability. To this end, this paper derives the locally weighted variants of standard regularization representation from Bayesian inference perspective, which impose the similarity constraint within the observed image and training images onto the penalty function. Further, considering the reduced sparseness of noisy images, a moderately sparse regularization method with a mixture of ℓ₁ and ℓ₂ norms is introduced to deal with noise robust face hallucination. New determination methods on weighting function and regularization parameter are particularly explored. Various experimental results on public face databases as well as real-world images validate the effectiveness of proposed method.