Model-aware learning for imaging inverse problems in fluorescence microscopy

Introduction

This project will develop model-aware, i.e. physics-informed, learning methods for solving imaging inverse problems (IIPs) in fluorescence microscopy imaging (FMI). IIPs are frequently encountered in FMI whenever a visual representation of a biological sample needs to be reconstructed from incomplete and noisy input measurements.

Problem Statement

Such IIPs are typically ill-posed: their solution (if it exists) is unstable to perturbations. Classical model-based approaches reformulate the IIP at hand as an energy minimisation task. These approaches rely on:

1. The (approximate) knowledge of the complex physical processes involved.
2. The mathematical design of hand-crafted optimisation methods whose tuning is often very time-consuming.

Current Developments

Concurrently, the impressive development of machine and deep learning methods has enabled the applied imaging community with new data-driven methodologies providing unprecedented results in tasks such as image classification.

Challenges

The performance of data-driven methods for solving IIPs in FMI, however, is halted by their intrinsic unstable behaviour.

Proposed Solution

In MALIN, I propose an integrative paradigm where the stable performance of model-based approaches is combined with the effectiveness of data-driven techniques by means of shallow model-constrained learning and deep physics-informed generative approaches.

Justification

The reliability of the model-aware methods proposed will be justified by theoretical results providing reconstruction and convergence guarantees.

Considerations

The study will further account for possible geometric invariances and imperfect physical modelling, showing robustness to modelling errors which are frequent when standard (low-cost) equipment is used.

Implementation Strategies

Algorithmic acceleration strategies and inexact/stochastic algorithms will be devised to guarantee efficient performance also under limited computational resources and training data.

Deployment

The methodologies will be deployed on several IIPs in FMI and democratised through the release of open software and plug-ins.