  In this two-part paper, we present a novel framework and methodology to
analyze data from certain image-based biochemical assays, e.g., ELISPOT and
Fluorospot assays. In this second part, we focus on our algorithmic
contributions. We provide an algorithm for functional inverse diffusion that
solves the variational problem we posed in Part I. As part of the derivation of
this algorithm, we present the proximal operator for the non-negative
group-sparsity regularizer, which is a novel result that is of interest in
itself, also in comparison to previous results on the proximal operator of a
sum of functions. We then present a discretized approximated implementation of
our algorithm and evaluate it both in terms of operational cell-detection
metrics and in terms of distributional optimal-transport metrics.
