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

arXiv: https://arxiv.org/abs/1810.03075 · HTML: https://mlsanity.com/paper/1810.03075/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2018.

## Built on by (most cited first, 3 of 3)

- [Deep Unrolled Recovery in Sparse Biological Imaging](https://mlsanity.com/paper/2109.14025/) (2021)
- [Joint Optimization of Hadamard Sensing and Reconstruction in Compressed Sensing Fluorescence Microscopy](https://mlsanity.com/paper/2105.07961/) (2021)
- [AdaptiveCDM: Source-Free Few-Shot Domain Adaptation for Cell Detection in Microscopic Images](https://mlsanity.com/paper/2503.03370/) (2025)

## Abstract (arXiv)

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 observation behind our algorithm is that cell detection task is 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 sparse coding) to compactly represent a variable number of cells in a projected space. Then, CNN regresses this compressed vector from the input microscopy image. Thanks to the SC/CS recovery algorithm (L1 optimization) that can 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 provides accuracy improvements over a training paradigm that treats CNN and CS-recovery layers separately. Our algorithm design also takes into account a form of ensemble average of trained models naturally to further boost accuracy of cell detection. We have validated our algorithm on benchmark datasets and achieved excellent performances.