Deconvolution! It holds out the promise of turning noisy, out-of-focus
images into tableaux of sparkling delight! And saving my PhD!
- As any fule kno, the classic algorithm is Richardson-Lucy; you
supply an image and a point spread function (you could estimate that
from the parameters of your microscope - but how? - or measure it by
imaging point sources, ie fluorescent subresolution beads), and it gives
you back a reconstructed image after a bunch of iterations.
- As with any iterative algorith, RL needs a stopping condition. The
traditional one is a chi-squared test
- If you believe what Matthias Pruksch and Frank Fleischmann have to
say about Positive
Iterative Deconvolution in Comparison to Richardson-Lucy Like
Algorithms, then RL may be better for point sources (eg stars), but
'positive iterative deconvolution' works better on detailed things (eg
- Then we've got the Expectation-maximization
algorithm, which is a development of RL. I get the impression that
EM is joint king of the hill with maximum entropy.
- The Wiener filter is, according to Mathworld, "an
optimal filter used for the removal of noise from a signal which is
corrupted by the measuring process itself", which sounds good, but
unlikely. A more
detailed description sheds more light; it's clever, elegant, but not
- M. D. Cahill's Unshake is nifty,
although probably not useful to me.
- On the question of unshaking, super-nifty results from Fergus,
Singh, Hertzmann, Roweis, and Freeman.. Lyndsey sent this to me, so
unsurprisingly, it's Bayesian.
- Richard L. White wrote about Image
Restoration Using the Damped Richardson-Lucy Method a while ago;
this is "a modification of the Richardson-Lucy iteration that reduces
noise amplification in restored images".
- The maximum
entropy method is a sophisticated form of deconvolution used in
- Dr Peter Steinbach has very kindly written An Introduction to the
Maximum Entropy Method which makes everything clear - this looks
very useful! In particular, the algorithm of Cornwell and Evans, with
tweaks, is the one we want.
- Molecular Expressions has a fairly high-level article on Algorithms
for Deconvolution Microscopy.
sounds interesting, but has fallen off the internet at the moment
- Scientific Volume Imaging's SVWiki has useful,
practical stuff (based on their Huygens software, but still of some
- Apple's vImage library has deconvolution
- A radioastronomy-oriented deconvolution
- A review on Iterative
methods for image deblurring - J. Biemond, R. L. Lagendijk, R. M.
Mersereau (May 1990); Proc IEEE 78(5):856
- Mathworks' tutorial on Deblurring
Images Using the Blind Deconvolution Algorithm, ie RL; has some
useful practical stuff.
Still haven't worked out if Tschumperlé-Deriche
vector-valued regularization PDEs (or, probably, its scalar, ie
monochrome, relatives) are any use.
PLAN OF ACTION: get or build implementations of Richardson-Lucy,
positive iterative, expectation maximisation and maximum entropy
filters, and run them over some sample data.
Back on the trail of MEM ...
- Maximum a posteriori estimation with Good's roughness for
three-dimensional optical-sectioning microscopy - S. Joshi, M. I. Miller
(1993); J Opt Soc Am A 10:1078
- Image restoration based on Good's roughness penalty with application
to fluorescence microscopy - P. J. Verveer, T. M. Jovin (1998); J Opt
Soc Am A 15:1077
- Artifacts in computational optical-sectioning microscopy - J. G.
McNally, C. Preza, J.-A. Conchello, L. J. Thomas Jr (1994); J Opt Soc Am
- A comparison of image restoration approaches applied to
three-dimensional confocal and wide-field fluorescence microscopy - P.
J. Verveer, M. J. Gemkow, T. M. Jovin (Jan 1999); J Microsc 193(1):50
Astronomy: Lecture #7; the first section deals with MEM and explains
it a bit more simply (but still with maths)
looks like magic.