Deconvolution by the Richardson-Lucy algorithm is achieved by minimizing the convex loss function derived in the last article
(1)
with
, the scalar quantity to minimize, function of ideal image
, linear captured image intensity laid out in
rows and
columns, corrupted by Poisson noise and blurred by the
, the known two-dimensional Point Spread Function that should be deconvolved out of
, the output image resulting from deconvolution, ideally without shot noise and blurring introduced by the
- ** two-dimensional convolution
element-wise product
, element-wise natural logarithm
In what follows indices and
, from zero to
-1 and
-1 respectively, are dropped for readability. Articles about algorithms are by definition dry so continue at your own peril.
So, given captured raw image blurred by known function
, how do we find the minimum value of
yielding the deconvolved image
that we are after?