Posted by
Lutz Schaefer on
Oct 31, 2011; 10:30pm
URL: http://confocal-microscopy-list.275.s1.nabble.com/Deconvolution-of-Confocal-Images-was-Airy-Units-tp6946310p6950050.html
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Dear Jim,
I do have a few problems with your recent statements:
> 1) It removes much of the effect of out-of-focus light (if there is any)
> and therefore produces a major improvement in the visibility of structures
> in widefield data. For confocal data, the resolution improvement is much
> less significant.
>
As deconvolution uses some inverse model of the forward problem
(convolution) it will not remove but re-assign intensities back to the
originating source. I am not sure if you remember the discussion with Walter
Carrington some time ago addressing this issue (or so he told me). It is in
fact even possible to use only out-of-focus information to reconstruct its
re-assigned in-focus contribution. Although this is not a preferable way to
do the processing, Walter demonstrated this case in his paper.
> 2) It effectively smooths the data out so that anything smaller than the
> PSF is removed from the processed result. This is good for two reasons:
>
This statement can be potentially misunderstood. Again, deconvolution is the
inverse of a convolution model. However, due to its ill-posed and
numerically instable nature, practical implementations need to employ what
is called regularization. Regularization can be understood as a form of
smoothing of the estimative solution. Depending on the actual amount of
noise present, improbable solutions will be excluded or made to no longer be
part of the set of probable solutions within the system of equations.
Depending on how the regularization is implemented and using various
a-priori information, this smoothing-part may or may not preserve edges
and/or intensities or other features. You can of course manually overweigh
the regularization term to do what you say, but normally there should be a
balance compromise between data fit and regularization. Deconvolution
typically increases uncorrelated statistical noise along with resolution and
contrast. This is, because the noise can not be easily modeled together with
a convolution operation. Maximum likelihood methods tend to increase the
noise lesser for which statistics they were designed for than others. I do
have a problem, accepting the statement that a deconvolution result is
equivalent to a convolution filter as you say. The often better SNR compared
to the observed data can only be the result of regularization. Usually
derivative based regularizations of varying orders are used, and they
therefore do not use the PSF as kernel. Lets say a Laplacian is used, then
the smoothing will generally be of Gaussian nature with variable sigma but
never confined to the PSF. And then again, as commercial systems these days
use a plethora of methods for regularizations (and useful combinations of
them), you can never say for sure, how the data will be smoothed, except
when looking at the mathematical model that was actually used.
> The decon process may seem to reduce image contrast (by averaging-down the
> bright noise peaks) but one can compensate for
Any deconvolution that works effectively (e.g is not over-regularized), will
in fact increase the contrast, as dictated by the 're-assignment' mentioned
above. Just imagine, simulating a microscope imaging forward problem with
just a simple lowpass filter. You will see, that the contrast from your
object declines after filtering. From a deconvolution you expect the
reverse, to get a good approximation to your original object, which had a
higher contrast to begin with.
I hope I have not stirred up more questions but there are good tutorials
available that describe deconvolution in greater detail.
Regards
Lutz
__________________________________
L u t z S c h a e f e r
Sen. Scientist
Mathematical modeling / Image processing
Advanced Imaging Methodology Consultation
16-715 Doon Village Rd.
Kitchener, ON, N2P 2A2, Canada
Phone/Fax: +1 519 894 8870
Email:
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___________________________________
--------------------------------------------------
From: "James Pawley" <
[hidden email]>
Sent: Monday, October 31, 2011 14:22
To: <
[hidden email]>
Subject: Re: Deconvolution of Confocal Images? (was: Airy Units)
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>
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>>
>>An interesting point was made here by Jim Pawley:
>>
>>>I agree that sampling a bit higher than Nyquist never hurts, especially
>>>if you deconvolve (as you always should), but I think that it is a
>>>mistake to think that one can "separate" out the noise by decon. I think
>>>that noise is pretty fundamental.
>>
>>I had always heard that if you're doing confocal microscopy, at least
>>point-scanning confocal with a pinhole size of 1AU or smaller, that
>>deconvolution was superfluous, because you shouldn't be getting out of
>>focus light. So what is gained by deconvolution when one is sampling voxel
>>by voxel?
>>
>>Peter G. Werner
>>Merritt College Microscopy Program
>
> Hi Peter,
>
> This is indeed "widely assumed". However, it is beside the point. The
> process of decon is applied to 3D, fluorescence microscopy data sets for
> (at least) two major different reasons:
>
> 1) It removes much of the effect of out-of-focus light (if there is any)
> and therefore produces a major improvement in the visibility of structures
> in widefield data. For confocal data, the resolution improvement is much
> less significant.
>
> 2) It effectively smooths the data out so that anything smaller than the
> PSF is removed from the processed result. This is good for two reasons:
>
> a) The process effectively averages the intensity data of the 64-125
> voxels needed to sample the central peak of the PSF, improving the S/N by
> a factor of between 8 and 11.
>
> b) It also meets the Nyquist Reconstruction Condition:
>
> If you have 2.5 pixels between the central peak and the first zero, you
> have 5 pixels across the diameter of the first-zero ring and (about) 25
> pixels will be needed to sample this blob in 2D and (about) 125 voxels in
> 3D. 125 measurements just to measure the brightness and location of one
> point. (The "about" has to do with how may counts one must register in a
> pixel for it to be considered part of the PSF, a PSF that will in general
> not be so conveniently aligned to the pixel grid. 100 might be a good
> guess for a 3D PSF.)
>
> But it is possible to "know" (measure?) the PSF independently, and the PSF
> imposes constraints on the relative brightness of these 125 points. Decon
> is the best process of imposing this constraint onto the measured data
> (For confocal, the 3D Gaussian mentioned earlier is a good approximation
> to the PSF. Although it is imprecise (it has a longer tail), if the
> Gaussian Laser beam doesn't considerably overfill the objective aperture,
> the spot will in fact be more like a Gaussian than an Airy disk. More to
> the point, the data are usually so Poisson-Noisy, that it won't make a
> great difference, and it is a lot easier to do.).
>
> The decon process may seem to reduce image contrast (by averaging-down the
> bright noise peaks) but one can compensate for this by changing the
> display look-up table (contrast control) and when you do this, you will
> find that the processed confocal data is far less noisy than was the raw
> data. It is also free from "impossible" features that were really only
> Poisson Noise excursions usually one-pixel wide (which is about 4 smaller
> than the width of the PSF, the smallest feature that the optical system
> can pass legitimately.). Indeed, one should never make statements
> regarding the exact shape of small structures (near the resolution limit)
> recorded in confocal microscopes until the data have been deconvolved.
> Nyquist would not approve.
>
> Best
>
> JP
> --
> ***************************************************************************
> Prof. James B. Pawley, Ph. 608-238-3953
> 21. N. Prospect Ave. Madison, WI 53726 USA
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