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 blurring 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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