  Learning rich data representations from unlabeled data is a key challenge
towards applying deep learning algorithms in downstream tasks. Several variants
of variational autoencoders (VAEs) have been proposed to learn compact data
representations by encoding high-dimensional data in a lower dimensional space.
Two main classes of VAEs methods may be distinguished depending on the
characteristics of the meta-priors that are enforced in the representation
learning step. The first class of methods derives a continuous encoding by
assuming a static prior distribution in the latent space. The second class of
methods learns instead a discrete latent representation using vector
quantization (VQ) along with a codebook. However, both classes of methods
suffer from certain challenges, which may lead to suboptimal image
reconstruction results. The first class suffers from posterior collapse,
whereas the second class suffers from codebook collapse. To address these
challenges, we introduce a new VAE variant, termed sparse coding-based VAE with
learned ISTA (SC-VAE), which integrates sparse coding within variational
autoencoder framework. The proposed method learns sparse data representations
that consist of a linear combination of a small number of predetermined
orthogonal atoms. The sparse coding problem is solved using a learnable version
of the iterative shrinkage thresholding algorithm (ISTA). Experiments on two
image datasets demonstrate that our model achieves improved image
reconstruction results compared to state-of-the-art methods. Moreover, we
demonstrate that the use of learned sparse code vectors allows us to perform
downstream tasks like image generation and unsupervised image segmentation
through clustering image patches.
