Three-Dimensional Image Reconstruction From Multi-Focus MicroscopyPublic Deposited
In this dissertation thesis, I introduce three-dimensional (3D) image reconstruction algorithms for multi-focus microscopy (MFM). MFM provides a fast way to obtain 3D information of the sample by simultaneously capturing multiple focal planes on a single camera shot. However, stacking the sub-images from different focal planes does not provide a good reconstruction of 3D image because of low signal-to-noise ratio (SNR) and severe out-of-focus blur of the microscopy. I analyze different models of the imaging process for MFM and derive multiple ways of 3D image reconstruction. First, I present image reconstruction methods based on models that assume Gaussian noise in the observation. As a base algorithm, I present a total-variation (TV) regularized least squares (RLS) algorithm for image reconstruction. We have developed two different algorithms to improve the performance of image reconstruction by using (1) multiple-frame processing, and (2) joint parameter estimation through a Bayesian framework, respectively. Multiple-frame processing utilizes the information from neighboring frames in addition to the current frame to improve the image quality. For joint parameter estimation, maximum-a-posteriori (MAP) is used for automatic estimation of the regularization parameter as well as 3D image reconstruction. Poisson noise model is also investigated to handle the low photon resource of MFM. For this, I present an alternating directions methods of multipliers (ADMM) based image reconstruction algorithm. This method splits the Poisson image deconvolution problem into two simpler problems - deblurring and Poisson denoising problems, providing an efficient way to solve the optimization problem. Experimental results with synthetic and real data verify the effectiveness of the methods.
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