A learning-based framework for representation of domain-specific images is proposed where joint compression and denoising can be done using a VQ-based multi-layer network. While it learns to compress the images from a training set, the compression performance is very well generalized on images from a test set. Moreover, when fed with noisy versions of the test set, since it has priors from clean images, the network also efficiently denoises the test images during the reconstruction. The proposed framework is a regularized version of the Residual Quantization (RQ) where at each stage, the quantization error from the previous stage is further quantized. Instead of codebook learning from the k-means which over-trains for high-dimensional vectors, we show that only generating the codewords from a random, but properly regularized distribution suffices to compress the images globally and without the need to resort to patch-based division of images. The experiments are done on the \textit{CroppedYale-B} set of facial images and the method is compared with the JPEG-2000 codec for compression and BM3D for denoising, showing promising results.