Computational Fluorescence Microscopy for Three Dimensional Reconstruction

Book excerpt: With rapidly increasing computational power, computational fluorescence microscopy is advancing the frontier of biological imaging. Computational algorithms tailored for specific experimental settings are demanded to solve given tasks such as denoising, spectral unmixing, 3D localization and reconstruction, and ptychography. In this thesis, we present the reconstruction of dense and sparse three dimensional fluorescent volumes. In the first half, we present a volumetric reconstruction method designed for 3D fluorescence imaging of biological samples in the low-light regime. Our method deconvolves a captured focal stack through optimization. As deconvolution is an ill-posed problem, the uniqueness of the solution is imposed through regularization. We formulate the objective function as a sum of a data fidelity term and a regularization term, and minimize it using the alternating direction method of multipliers algorithm. The data fidelity is accurately evaluated with a negative log-likelihood function based on a mixed Poisson-Gaussian model of photon shot noise and camera read noise, which are both present in low-light imaging. Among several possible regularization strategies, we show that a Hessian-based regularizer is most effective for describing locally smooth features present in biological specimens. We demonstrate its performance for fixed and live cell imaging, showing its applicability as a tool for biological research. In the second half, we introduce a hybrid optical-electronic computing approach to three dimensional localization microscopy. Driven by artificial intelligence, this approach learns a set of depth-dependent point spread functions (PSFs) and a localization network jointly in an end-to-end fashion, co-designing an optical imaging system and a neural network. We also present a custom grayscale lithography process to fabricate freeform diffractive optical elements that optically implement the designed PSFs and outline several biological experiments with fixed and live cells that demonstrate the efficacy of the proposed computational microscopy approach.