As far as I understand this, these guys claim they can train convolutional and many other types of deep neural nets faster by pretraining each layer with a new unsupervised technique via which the layer sort of learns to compress its inputs (a local optimization problem), and then they fine tune the whole network end-to-end with supervised SGD and backpropagation as usual. They have not released code, so no one else…
The paper presents these and other approaches as being instances of a classical, general form, regularized regression but with the "stacked" property involving each layer iterating however many times and then the next layer changing parameters (or features) and further iterating.
From my barely-informed viewpoint, this sounds like a fascinating way to unify the earlier efforts and one which could yield a variety of other approaches - even if the particular variation they use doesn't work out. But I assume lots of more-informed people are going to be looking at this.