Cell detection by functional inverse diffusion and non-negative group sparsity
Pol del Aguila Pla, KTH Royal Institute of Technology

Seminar • 07 May 2019

Abstract
Image-based immunoassays are designed to estimate the proportion of biological cells in a sample that generate a specific kind of particles. These assays are instrumental in biochemical, pharmacological and medical research, and have applications in disease diagnosis. In this talk, I describe the model, inverse problem, functional optimization framework, and algorithmic solution to analyze image-based immunoassays that we presented in [1] and [2]. In particular, I will delve into 1) the radiation-diffusion-adsorption-desorption partial differential equation and a re-parametrization of its solution in terms of convolutional operators, 2) the set up, analysis and algorithmic solution of an optimization problem in Hilbert spaces to recover spatio-temporal information from a single image observation, and 3) the derivation of the proximal operator in function spaces for the non-negative group-sparsity regularizer. After discretization, our work results in a convergent, high-performing algorithm with 25 million optimization variables that requires the entire engineering toolbox of tips and tricks, and was recently incorporated in a commercial product [3]. If time allows, I will introduce our work in [4], in which we use the structure of our algorithm to learn a faster, approximated solver for our optimization problem. [1]: Pol del Aguila Pla and Joakim Jaldén, "Cell detection by functional inverse diffusion and non-negative group sparsity Part I: Modeling and Inverse Problems", IEEE Transactions on Signal Processing, vol. 66, no. 20, pp. 5407-5421, 2018. Access at: https://doi.org/10.1109/TSP.2018.2868258 [2]: Pol del Aguila Pla and Joakim Jaldén, "Cell detection by functional inverse diffusion and non-negative group sparsityPart II: Proximal optimization and Performance Evaluation", IEEE Transactions on Signal Processing, vol. 66, no. 20, pp. 5422-5437, 2018. Access at: https://doi.org/10.1109/TSP.2018.2868256 [3]: Mabtech Iris reader. See product page: https://www.mabtech.com/iris [4]: Pol del Aguila Pla, Vidit Saxena, and Joakim Jaldén, "SpotNet Learned iterations for cell detection in image-based immunoassays", 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019). Access at: https://arxiv.org/abs/1810.06132