  The Residual Quantization (RQ) framework is revisited where the quantization
distortion is being successively reduced in multi-layers. Inspired by the
reverse-water-filling paradigm in rate-distortion theory, an efficient
regularization on the variances of the codewords is introduced which allows to
extend the RQ for very large numbers of layers and also for high dimensional
data, without getting over-trained. The proposed Regularized Residual
Quantization (RRQ) results in multi-layer dictionaries which are additionally
sparse, thanks to the soft-thresholding nature of the regularization when
applied to variance-decaying data which can arise from de-correlating
transformations applied to correlated data. Furthermore, we also propose a
general-purpose pre-processing for natural images which makes them suitable for
such quantization. The RRQ framework is first tested on synthetic
variance-decaying data to show its efficiency in quantization of
high-dimensional data. Next, we use the RRQ in super-resolution of a database
of facial images where it is shown that low-resolution facial images from the
test set quantized with codebooks trained on high-resolution images from the
training set show relevant high-frequency content when reconstructed with those
codebooks.
