3D Microscopy Deconvolution using Richardson-Lucy Algorithm with Total Variation Regularization

Confocal laser scanning microscopy is a powerful and increasingly popular technique for 3D imaging of biological specimens. However the acquired images are degraded by blur from out-of-focus light and Poisson noise due to photon-limited detection. Several deconvolution methods have been proposed to reduce these degradations, including the Richardson-Lucy iterative algorithm, which computes a maximum likelihood estimation adapted to Poisson statistics. However this algorithm does not necessarily converge to a suitable solution, as it tends to amplify noise. If it is used with a regularizing constraint (some prior knowledge on the data), Richardson-Lucy regularized with a well-chosen constraint, always converges to a suitable solution. Here, we propose to combine the Richardson-Lucy algorithm with a regularizing constraint based on Total Variation, whose smoothing avoids oscillations while preserving object edges. We show on simulated and real images that this constraint improves the deconvolution results both visually and using quantitative measures. We compare several well-known deconvolution methods to the proposed method, such as standard Richardson-Lucy (no regularization), Richardson-Lucy with Tikhonov-Miller regularization, and an additive gradient-based algorithm.