Tuning Sparsity for Face Hallucination Representation

Due to the under-sparsity or over-sparsity, the widely used regularization methods, such as ridge regression and sparse representation, lead to poor hallucination performance in the presence of noise. In addition, the regularized penalty function fails to consider the locality constraint within the observed image and training images, thus reducing the accuracy and stability of optimal solution. This paper proposes a locally weighted sparse regularization method by incorporating distance-inducing weights into the penalty function. This method accounts for heteroskedasticity of representation coefficients and can be theoretically justified from Bayesian inference perspective. Further, in terms of the reduced sparseness of noisy images, a moderately sparse regularization method with a mixture of ‘1 and ‘2 norms is introduced to deal with noise robust face hallucination. Various experimental results on public face database validate the effectiveness of proposed method.