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Hi everyone,

After reading many articles, books and lots of playing around with 
algorithms, the unknowns about 2D-Deconvolution seem to accumulate rather 
than to disappear.
Since I´m not sure whether I´m still on the right track, I thought I drop a 
few lines in this excellent forum, hopefully someone can help.

Leaving aside other fancy features and for the sake of simpleness; I set up 
a widefield scope for live-imaging with pulsed dual laser excitation by 
AOMs, an EM-CCD camera, no piezo driven stage and a 60x water objective. 
Before seriously starting to investigate biological matters, I remembered 
the statement, which I also came across with in James Pawley´s recent book: 
"Deconvolve everything!!".
I´m not an expert in Deconvolution and never ran it myself before, so would 
you experienced "Deconvolutionists" agree that it´s worthy for 2D-images?
2D-Deconvolution would clearly be limited compared to "ideal" 
3D-Deconvolution, since one does not have the information from adjacent 
planes. Thus, it´s quite inaccurate if not even impossible to remove out of 
focus light, isn´t it? On the other hand, one could still recover high 
spatial frequencies which were attenuated by the OTF (actually by the NA) 
and not to forget removing Poisson noise. Is the noise removal due to the 
fact that features smaller than the PSF size will be neglected during 
Deconvolution or because the spatial frequency of noise is most likely to 
be out of the OTF limit (2NA/lambda and NA²/(2*n*lambda)? Is there a 
reference at what range of frequencies noise would be expected or is it 
rather evenly distributed (i.e. when looking at the Fourier-transform of an 
image)?

Due to the missing automated stage I can´t record the PSF of my system. 
Normally one records the PSF/OTF at the actual system, basically to include 
eventual misalignment, underfilling of the back aperture etc. If I remember 
correctly, I think the Deltavision guys measure the objectives separately 
and use this measured PSF for Deconvolution (leaving blind-decon aside for 
now). Is this because of the high precision of their scope, hence 
eliminating eventual misalignment effects on the OTF? What are general 
experiences in terms of measuring an objective´s PSF at a different system 
compared to the "real" one in the actual scope (spherical abberations, 
asymmetric shapes)?

As to deconvolution results. How can one judge whether an algorithm 
produced a correct result? Obviously, an experienced eye will see most of 
the artifacts, but what are objective, reliable and measurable 
characteristics in order to say that this image has been improved or that 
one is clearly ruined? Signal-to-noise-Ratio, Fourier analysis, Image 
properties (i.e. speckles, ringing effects)?
What is an appropriate way for defining the S/N-ratio for images? I ran 
across many different methods,such as: mean(I)/std(I) or max(I)/std(I) or 
maybe applying a morphological operation, distinguishing signal and 
background and then mean(signal)/sqrt(mean(noise)+mean(signal)). Which one 
is a commonly accepted method for S/N calculation in image processing?

With respect to appropriate Deconvolution algorithms, essentially all 
references say that iterative algorithms are superior to linear filters 
(due to applying constraints (i.e. non-negativity), not a simple high-pass 
filter, etc.).  Because of the missing PSF in my particular case, 
Blind-Decon seems to be the right choice. Or does someone disagree on that one?
Applying the blind-deconvolution in Matlab to various images of 
fluorescently stained cells, also having different noise levels, revealed 
rather disappointing results. The higher the iteration steps (more than 10 
iterations), the more speckled the images became. Strangely, the magnitude 
of the fourier-transfered image always tends to form a weird symmetrical 
pattern (I´m happy to send to images for those interested). Varying the 
inital PSF-size doesn´t help either and the reconstructed image becomes 
increasingly noisy after more than 15 iterations. Does someone know about 
this problem? Did someone already successfully deconvolve 2D data with 
Matlab? The only reason I could think of is that my system is far away from 
being perfectly aligned and thus leading to "non-reconstructable" images. 
Due to the missing stage, I can´t check that issue. However, from my 
understanding the blind deconvolution should be able to deal with 
asymmetric PSFs (if it´s not too far off). Any further ideas?

Another simple question that´s still in my head. When referring to the 
lateral size of the PSF, is it the distance of the 1st two minima around 
the AiryDisc, or the size with further minima, the FWHM, or simply by 
practical approach - the diameter in pixels of a subresolution bead in focus?

Well, that post became quite long. Sorry for asking so many questions at once.

Many, many thanks in advance for any input, it´ll be very much appreciated!


Best regards,

Steffen Steinert, Dipl.-Ing.

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Universität Stuttgart
3. Physikalisches Institut
Pfaffenwaldring 57
70550 Stuttgart

Tel.: 49/711/68565230
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