Deconvolution of 3D Fluorescence Microscopy Images using Scaled Gradient Methods

Abstract

Fluorescence microscopy images are blurred due to diffraction of light by passage through the optical path of the microscope. The resulting image is the convolution of the original object with a point spread function. We investigate the restoration of 3D fluorescence microscopy images that are affected by convolution and noise. We use a variational approach and investigate both which functional to minimize and how to find the minimizer. Regularization reflects a trade-off between bias and variance that is controlled by the regularization parameter. We apply different methods for finding the optimal value for this parameter and investigate how the optimal value depends on the signal-to-noise ratio of the image. We minimize the functional by using a scaled gradient projection algorithm that aims to improve the convergence rate compared to a standard gradient descent method by multiplication of the search direction by a scaling matrix and choosing an effective step size. The algorithm is applied to real data from confocal and widefield microscopy. The convergence of the algorithm is investigated and different scaling matrices are compared.