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?
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