The Richardson–Lucy algorithm, also known as Lucy–Richardson deconvolution, is an iterative procedure for recovering a latent image that has been blurred by a known point spread function. It was named after William Richardson and Leon Lucy, who described it independently.
Description
When an image is recorded on a detector such as photographic film or a charge coupled device, it is generally slightly blurred, with an ideal point source not appearing as a point but being spread out, into what is known as the point spread function. Non-point sources are effectively the sum of many individual point sources, and pixels in an observed image can be represented in terms of the point spread function and the latent image as
where
The basic idea is to calculate the most likely
where
It has been shown empirically that if this iteration converges, it converges to the maximum likelihood solution for
This can also be written more generally (for more dimensions) in terms of convolution,
where the division and multiplication are element wise, and
In problems where the point spread function