We propose a general method for semantic representation of images and other
data using progressive coding. Semantic coding allows for specific pieces of
information to be selectively encoded into a set of measurements that can be
highly compressed compared to the size of the original raw data. We consider a
hierarchical method of coding where a partial amount of semantic information is
first encoded a into a coarse representation of the data, which is then refined
by additional encodings that add additional semantic information. Such
hierarchical coding is especially well-suited for semantic communication i.e.
transferring semantic information over noisy channels. Our proposed method can
be considered as a generalization of both progressive image compression and
source coding for semantic communication. We present results from experiments
on the MNIST and CIFAR-10 datasets that show that progressive semantic coding
can provide timely previews of semantic information with a small number of
initial measurements while achieving overall accuracy and efficiency comparable
to non-progressive methods