  In this work, we propose the Sparse Multi-Family Deep Scattering Network
(SMF-DSN), a novel architecture exploiting the interpretability of the Deep
Scattering Network (DSN) and improving its expressive power. The DSN extracts
salient and interpretable features in signals by cascading wavelet transforms,
complex modulus and extract the representation of the data via a
translation-invariant operator. First, leveraging the development of highly
specialized wavelet filters over the last decades, we propose a multi-family
approach to DSN. In particular, we propose to cross multiple wavelet transforms
at each layer of the network, thus increasing the feature diversity and
removing the need for an expert to select the appropriate filter. Secondly, we
develop an optimal thresholding strategy adequate for the DSN that regularizes
the network and controls possible instabilities induced by the signals, such as
non-stationary noise. Our systematic and principled solution sparsifies the
network's latent representation by acting as a local mask distinguishing
between activity and noise. The SMF-DSN enhances the DSN by (i) increasing the
diversity of the scattering coefficients and (ii) improves its robustness with
respect to non-stationary noise.
