In (Hao et al. 2012), we propose a novel model in the deep learning framework concentrated specifically on textures in images. The model is a convolutional variant of the Gaussian gated Boltzmann machine inspired by a so called co-occurrence matrix in traditional texture analysis. This model is also applicable to both classification and reconstruction tasks.
We have used small images as example data while developing new models and methods in deep learning in general. For instance, in (Raiko et al. 2012), we showed competitive classification performance of small images with very low computational complexity. Deep learning models are often applicable to both classification and reconstruction tasks at once. An example of image reconstruction can be found in (Cho et al. 2011), where left half of a face is reconstructed from the right half (see figure) using a model learned from full images of other people..
There is one master's thesis written on image-specific models: