**Abstract**

Image-based immunoassays are used every day across the world to develop new drugs, diagnose diseases, and research the workings of the human body. Since August, some of these are analyzed by technology that, at its core, has an algorithm included in my Ph.D. work. In this talk, I will outline the research project that lead to this algorithm and go through the modeling and optimization results we present in [1] and [2]. This will include, among others, the modeling of complex biochemical assays as systems of partial differential equations, a linear-systems view on diffusion models, investigations in group-sparsity regularization in function spaces, and first-order methods for optimization problems with more than 25 million variables. To conclude the presentation, I will go through the new paths we have started to explore in connecting all this work to deep learning frameworks [3].

[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

[2]: Pol del Aguila Pla and Joakim Jaldén, “Cell detection by functional inverse diffusion and non-negative group sparsity—Part II: Proximal optimization and Performance Evaluation”, IEEE Transactions on Signal Processing, vol. 66, no. 20, pp. 5422–5437, 2018

[3]: Pol del Aguila Pla, Vidit Saxena, and Joakim Jaldén, “SpotNet – Learned iterations for cell detection in image-based immunoassays”, Submitted to the 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019), arXiv: 1810.06132 [eess.SP]