Computational methods for 3D imaging of neural activity in light-field microscopy

Abstract

Light Field Microscopy (LFM) is a 3D imaging technique that captures spatial and angular information from light in a single snapshot. LFM is an appealing technique for applications in biological imaging due to its relatively simple implementation and fast 3D imaging speed. For instance, LFM can help to understand how neurons process information, as shown for functional neuronal calcium imaging. However, traditional volume reconstruction approaches for LFM suffer from low lateral resolution, high computational cost, and reconstruction artifacts near the native object plane. Therefore, in this thesis, we propose computational methods to improve the reconstruction performance of 3D imaging for LFM with applications to imaging neural activity.

First, we study the image formation process and propose methods for discretization and simplification of the LF system. Typical approaches for discretization are performed by computing the discrete impulse response at different input locations defined by a sampling grid. Unlike conventional methods, we propose an approach that uses shift-invariant subspaces to generalize the discretization framework used in LFM. Our approach allows the selection of diverse sampling kernels and sampling intervals. Furthermore, the typical discretization method is a particular case of our formulation.

Moreover, we propose a description of the system based on filter banks that fit the physics of the system. The periodic-shift invariant property per depth guarantees that the system can be accurately described by using filter banks. This description leads to a novel method to reduce the computational time using singular value decomposition (SVD). Our simplification method capitalizes on the inherent low-rank behaviour of the system. Furthermore, we propose rearranging our filter-bank model into a linear convolution neural network (CNN) that allows more convenient implementation using existing deep-learning software.

Then, we study the problem of 3D reconstruction from single light-field images. We propose the shift-invariant-subspace assumption as a prior for volume reconstruction under ideal conditions. We experimentally show that artifact-free reconstruction (aliasing-free) is achievable under these settings. Furthermore, the tools developed to study the forward model are exploited to design a reconstruction algorithm based on ADMM that allows artifact-free 3D reconstruction for real data. Contrary to traditional approaches, our method includes additional priors for reconstruction without dramatically increasing the computational complexity. We extensively evaluate our approach on synthetic and real data and show that our approach performs better than conventional model-based strategies in computational time, image quality, and artifact reduction.

Finally, we exploit deep-learning techniques for reconstruction. Specifically, we propose to use two-photon imaging to enhance the performance of LFM when imaging neurons in brain tissues. The architecture of our network is derived from a sparsity-based algorithm for reconstruction named Iterative Shrinkage and Thresholding Algorithm (ISTA). Furthermore, we propose a semi-supervised training based on Generative Adversarial Neural Networks (GANs) that exploits the knowledge of the forward model to achieve remarkable reconstruction quality. We propose efficient architectures to compute the forward model using linear CNNs. This description allows fast computation of the forward model and complements our reconstruction approach. Our method is tested under adverse conditions: lack of training data, background noise, and non-transparent samples. We experimentally show that our method performs better than model-based reconstruction strategies and typical neural networks for imaging neuronal activity in mammalian brain tissue. Our approach enjoys both the robustness of the model-based methods and the reconstruction speed of deep learning.