Tag Archives: LR

The Richardson-Lucy Algorithm

Deconvolution by the Richardson-Lucy algorithm is achieved by minimizing the convex loss function derived in the last article

(1)   \begin{equation*} J(O) = \sum \bigg (O**PSF - I\cdot ln(O**PSF) \bigg) \end{equation*}

with

  • J, the scalar quantity to minimize, function of ideal image O(x,y)
  • I(x,y), linear captured image intensity laid out in M rows and N columns, corrupted by Poisson noise and blurred by the PSF
  • PSF(x,y), the known two-dimensional Point Spread Function that should be deconvolved out of I
  • O(x,y), the output image resulting from deconvolution, ideally without shot noise and blurring introduced by the PSF
  • **   two-dimensional convolution
  • \cdot   element-wise product
  • ln, element-wise natural logarithm

In what follows indices x and y, from zero to M-1 and N-1 respectively, are dropped for readability.  Articles about algorithms are by definition dry so continue at your own peril.

So, given captured raw image I blurred by known function PSF, how do we find the minimum value of J yielding the deconvolved image O that we are after?

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Raw Converter Sharpening with Sliders at Zero?

I’ve mentioned in the past that I prefer to take spatial resolution measurements directly off the raw information in order to minimize often unknown subjective variables introduced by demosaicing and rendering algorithms unbeknownst to the operator, even when all relevant sliders are zeroed.  In this post we discover that that is indeed the case for ACR/LR process 2010/2012 and for Capture NX-D – while DCRAW appears to be transparent and perform straight out demosaicing with no additional processing without the operator’s knowledge.

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