  Deep learning is a hot research topic in the field of machine learning
methods and applications. Generative Adversarial Networks (GANs) and
Variational Auto-Encoders (VAEs) provide impressive image generations from
Gaussian white noise, but both of them are difficult to train since they need
to train the generator (or encoder) and the discriminator (or decoder)
simultaneously, which is easy to cause unstable training. In order to solve or
alleviate the synchronous training difficult problems of GANs and VAEs,
recently, researchers propose Generative Scattering Networks (GSNs), which use
wavelet scattering networks (ScatNets) as the encoder to obtain the features
(or ScatNet embeddings) and convolutional neural networks (CNNs) as the decoder
to generate the image. The advantage of GSNs is the parameters of ScatNets are
not needed to learn, and the disadvantage of GSNs is that the expression
ability of ScatNets is slightly weaker than CNNs and the dimensional reduction
method of Principal Component Analysis (PCA) is easy to lead overfitting in the
training of GSNs, and therefore affect the generated quality in the testing
process. In order to further improve the quality of generated images while keep
the advantages of GSNs, this paper proposes Generative Fractional Scattering
Networks (GFRSNs), which use more expressive fractional wavelet scattering
networks (FrScatNets) instead of ScatNets as the encoder to obtain the features
(or FrScatNet embeddings) and use the similar CNNs of GSNs as the decoder to
generate the image. Additionally, this paper develops a new dimensional
reduction method named Feature-Map Fusion (FMF) instead of PCA for better
keeping the information of FrScatNets and the effect of image fusion on the
quality of image generation is also discussed.
