Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity-Part II: Proximal Optimization and Performance Evaluation

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.