Deconvolving spectral images

Spectral imaging refers to the acquisition of several Emission Wavelengths from the same fluorescent object to register a spectrum of the emission.

One can for example acquire emission wavelengths from 500 to 700 nm in 1 to 10 nm difference, obtaining up to 20-100 images from the same cell.

If there are let's say two fluorophores on the cell, with partially overlapping emission spectra, one can in principle (specially if the independent spectra are known) separate the two contributions from the acquired spectrum and calculate the contribution of each dye to each pixel's intensity. This is called unmixing.

The unmixing of the acquired channels is also called spectral deconvolution, not to confound with the DeConvolution concerning the Point Spread Function (PSF).

The question is how to restore such a dataset. Must you do first PSF deconvolution and then unmixing or vice versa?

Noise free case

A noise free image would be certainly rare in a Fluorescence Microscope. The amount of acquired photons is usually low, but when you split them among many channels each channel gets even less photons. Because the noise is mostly Photon Noise, the Signal To Noise Ratio (SNR) per channel decreases with the number of acquired photons!!!

Anyway, if your system provides noise free images, then the question is whether the PSF is different per channel or not. The Huygens Software can help you in most of these cases.

PSF is wavelength independent

In this case the deconvolution order doesn't matter very much. You can first use the PSF to do blur deconvolution and then unmix, or the other way around. Unmixing first will probably leave less channels for deconvolution, that can be smart.

PSF is wavelenght dependent

If the PSF varies only fairly depending on the wavelength, then you can still consider separating both deconvolutions with little error. Still it is a better idea to unmix first and then use the PSF. Being the PSF deconvolution a Non Linear procedure (a Non Linear Iterative Method), it is not smart to apply it prior to the linear unmixing.

If the PSF is very different at different wavelenghts, then the answer is the same as in the noisy case explained below.

Noisy case

The correct answer now is that both deconvolutions should be done simultaneously!!! That is the only way to make sure that the noise is properly handled, combining the Non Linear PSF deconvolution with the linear unmixing. Many deconvolution algorithms must run in parallel, one per dye (not per channel!!!), to estimate in each iteration the distribution of each dye inside the image.

Currently the Huygens Software is not prepared to do that. It can deconvolve many channels (up to 32), but always considering that they are independent, free of Cross Talk.

Notes

These are some discussion notes about the topic between some users and SVI:

A

> The main issue is how to treat as much as 32 channel images and how to

> measure PSF by spectral means, as I wrote you last time, I was not able

> to find any reference literature to this issue.

I''n the London's Microscience some weeks ago I asked people from a manufacturer how do they deal with noise during spectral deconvolution, and I didn't get a clear answer, but I'm afraid that spectral microscopy can introduce many noise problems in confocal images, that are already noisy enough: having few photons, the SNR will decrease a lot if you split these over different detectors!!!

You addressed some interesting points:''

B

> How to deal with more than 4 channels in Huygens?

''As I told you, opening up to 32 channels shouldn't be a problem in
the Huygens Software. Please tell me if anything fails here. Deconvolving each
channel with a Theoretical Psf could be a good test to start with.''

C

> How to measure a PSF for these spectral data?

''Your beads should provide enough intensity in all detection channels
to have a good SNR. If the emission spectrum of the bead doesn't cover
all the detection channels, you must use a multicolor bead or another
bead. But detection intensity doesn't have to be constant per channel,
because the PSF will be normalized in any case during its
__distillation.''

D

> The unmixed images are result of image processing based on an algorithm,

> properties of which are known only to its author (Nikon in our case). So

> my question was: How would you treat such images. They do not posses

> properties of directly acquired images, with respect to additional image

> analysis. Colocalization statistics especially. The pixel intensities

> were modified etc.

''Ideally after the two deconvolutions (first the
wavelength unmixing, then the PSF deconvolution, when they can't be done simultaneously) you would
get a good (i.e. realistic) distribution of intensities where you can
apply coloc analysis. Any analysis that lacks any of these two
deconvolutions wouldn't be very trustful. But then my previous
question applies again: why doing spectral unmixing at all? Is it to
correct for crosstalk? I think that then it would be much better to do
just two channel measurements of the colocalizing signals, not
simultaneously but switching excitations alternatively. Even if the
emission spectra overlap, you could use dyes where the excitation
don't, and you will be sure that the recorded signal comes from a
given dye only each time. Even if some overlap exists you could
calibrate it and correct (unmix) the two channels. Than would surely
be less sensitive to noise than splitting the signal over 32 detection
channels. I can only understand spectral measurements where the
excitation of both dyes is unavoidably simultaneous. This the case
of your experiment so crosstalk is unfortunately unavoidable!''

E

> In case of spectrally unmixed data – what should we choose in terms of imaging properties for those channels (exc/em, etc)? All the same values?

• Use the laser wave lenghst as excitation wavelenghts. Use the laser wave lenghst as excitation wavelenghts. Use the laser wave lenghst as excitation wavelenghts. Use the laser wave lenghst as excitation wavelenghts.
• Use the wavelenght of the renamed pseudo colors as emission wavelenghts. Probably that value will lay around the theoretical emission wavelenght of the fluophore.''