Training Convolutional Neural Networks and Compressed Sensing End-to-End for Microscopy Cell Detection

Automated cell detection and localization from microscopy images are significant tasks in biomedical research and clinical practice. In this paper, we design a new cell detection and localization algorithm that combines deep convolutional neural network (CNN) and compressed sensing (CS) or sparse coding (SC) for end-to-end training. We also derive, for the first time, a backpropagation rule, which is applicable to train any algorithm that implements a sparse code recovery layer. The key innovation behind our algorithm is that the cell detection task is structured as a point object detection task in computer vision, where the cell centers (i.e., point objects) occupy only a tiny fraction of the total number of pixels in an image. Thus, we can apply compressed sensing (or equivalently SC) to compactly represent a variable number of cells in a projected space. Subsequently, CNN regresses this compressed vector from the input microscopy image. The SC/CS recovery algorithm ( ${L} _{1}$ optimization) can then recover sparse cell locations from the output of CNN. We train this entire processing pipeline end-to-end and demonstrate that end-to-end training improves accuracy over a training paradigm that treats CNN and CS-recovery layers separately. We have validated our algorithm on five benchmark datasets with excellent results.