Fastfood dictionary learning for periocular-based full face hallucination

The kernel trick becomes a burden for some machine learning tasks such as dictionary learning, where a huge amount of training samples are needed, making the kernel matrix gigantic and infeasible to store or process. In this work, we propose to alleviate this problem and achieve Gaussian RBF kernel expansion explicitly for dictionary learning using Fastfood transform, which is an approximation of full kernel expansion. We have shown, in the context of missing data recovery through joint dictionary learning i.e. periocular-based full face hallucination, that the approximated kernel expansion using Fastfood transform for joint dictionary learning yields much better results than its image space counterparts. Also, explicit kernel expansion through Fastfood allows us to de-kernelize the reconstructed image in the feature space back to the image space, enabling applications that require reconstructive dictionaries such as cross-domain reconstruction, image super-resolution, missing data recovery, etc.