  We propose a new approach to Generative Adversarial Networks (GANs) to
achieve an improved performance with additional robustness to its so-called and
well recognized mode collapse. We first proceed by mapping the desired data
onto a frame-based space for a sparse representation to lift any limitation of
small support features prior to learning the structure. To that end we start by
dividing an image into multiple patches and modifying the role of the
generative network from producing an entire image, at once, to creating a
sparse representation vector for each image patch. We synthesize an entire
image by multiplying generated sparse representations to a pre-trained
dictionary and assembling the resulting patches. This approach restricts the
output of the generator to a particular structure, obtained by imposing a Union
of Subspaces (UoS) model to the original training data, leading to more
realistic images, while maintaining a desired diversity. To further regularize
GANs in generating high-quality images and to avoid the notorious mode-collapse
problem, we introduce a third player in GANs, called reconstructor. This player
utilizes an auto-encoding scheme to ensure that first, the input-output
relation in the generator is injective and second each real image corresponds
to some input noise. We present a number of experiments, where the proposed
algorithm shows a remarkably higher inception score compared to the equivalent
conventional GANs.
