Abstract

Computational optical sectioning is a method for reconstructing 3-D images of living biological structures from data acquired via light microscopy as a series of 2-D images taken along the optical axis of the microscope. Each 2-D image is corrupted with light from out-of-focus regions. This effect can be modeled as the 3-D convolution of the specimen with the microscope’s point-spread function. The problem is to determine the object’s intensity in terms of the measured data quickly enough for interactive use and for time-lapse analyses. The linear least-squares solution can be obtained rapidly by inverse filtering, but the problem is ill-posed in view of the inversion of small eigenvalues of the point-spread function operator. We have regularized the problem by application of the linear-precision-gauge formalism of Joyce and Root.¹ The linear least-squares solution is constrained to lie in a subspace corresponding to a selected number of large eigenvalues. The tradeoff between the variance of the solution and the regularization error determines the number of inverted eigenvalues. The resulting linear method is a fast one-step algorithm with computational complexity of the order of the FFT. The method is robust to noise and to underestimation of the width of the point-spread function.

© 1991 Optical Society of America