  We study sparsification of convolutional neural networks (CNN) by a relaxed
variable splitting method of $\ell_0$ and transformed-$\ell_1$ (T$\ell_1$)
penalties, with application to complex curves such as texts written in
different fonts, and words written with trembling hands simulating those of
Parkinson's disease patients. The CNN contains 3 convolutional layers, each
followed by a maximum pooling, and finally a fully connected layer which
contains the largest number of network weights. With $\ell_0$ penalty, we
achieved over 99 \% test accuracy in distinguishing shaky vs. regular fonts or
hand writings with above 86 \% of the weights in the fully connected layer
being zero. Comparable sparsity and test accuracy are also reached with a
proper choice of T$\ell_1$ penalty.
