Deconvolution - Richardson Lucy vs. Wiener Filter
Both are the MMSE estimators.

The main difference is Wiener is the optimal for Gaussian Noise while Richardson Lucy assumes Poisson Noise.

Poisson Noise is a better model for noise in photos captured by a Photo Diode.

Computationally, in the case of Gaussian Noise and Linear Convolution the solution has a closed form solution in the Maximum Likelihood / LS sense.

The Lucy Richardson method, which is a Maximum Likelihood in the Poisson case, has no closed form solution and requires iterative approach.

See Noise, Image Reconstruction with Noise (EE367/CS448I: Computational Imaging and Display, Class 10, Gordon Wetzstein, Stanford University).