median filtering confocal microscope data at the instrument

[Lutz Schaefer]

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Guy,
I was under the impression (and perhaps this being my bad), that the here
always discussed photon count was meant as "information about the ground
truth signal" and the PSF is "some partial a-priori knowledge about the
forward model". Both exist independent from each other and are two
completely different functional information aspects in image formation, that
you can't "mingle" together. Obviously "information" being an abstract term,
it demonstrates the intriguing confusion it may cause in any discussion,
especially if you think exclusively in terms of the sample's fluorescent
signal that you are actually interested in. Strictly, the PSF itself does
not explain image formation, you need to understand the integral equation
(special case: convolution that may apply approximately) behind it, leading
to the observation. This is yet another piece of information. How do you
weigh all these information components to make sense in a discussion that
focuses on intensities?

Regards
Lutz


--------------------------------------------------
From: "Guy Cox" <[hidden email]>
Sent: Saturday, March 02, 2013 03:15
To: <[hidden email]>
Subject: Re: median filtering confocal microscope data at the instrument

> Lutz,
>
>            Are you really equating intensity with information?  In a post
> about using accurate language to describe mathematical operations, this
> seems surprising.
>
>                                                                  Guy
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:[hidden email]]
> On Behalf Of Lutz
> Sent: Saturday, 2 March 2013 6:22 AM
> To: [hidden email]
> Subject: Re: median filtering confocal microscope data at the instrument
>
> Johannes
> verbal interpretation of a mathematical matter is almost always incorrect.
> One has to be very careful not to be misunderstood. For example when you
> say that information gets stripped out of a widefield image is incorrect
> for deconvolution. In fact the inverse of a convolution will add
> intensities back into point objects. I cannot see how that reduces
> information content. My point is just to be careful when mathematical
> expressions become interpreted verbally. You likely loose information
> there too especially if the context isnt understood.
>
> My 2 cents
> Regards
> Lutz
>
> Sent from Samsung Mobile
>
> -------- Original message --------
> Subject: Re: median filtering confocal microscope data at the instrument
> From: Johannes Schindelin <[hidden email]>
> To: [hidden email]
> CC:
>
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> [Sorry, reposting with the subscribed mail address]
>
> On Fri, 1 Mar 2013, Johannes Schindelin wrote:
>
>> *****
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>>
>> Hi Guy,
>>
>> On Wed, 27 Feb 2013, Guy Cox wrote:
>>
>> > The term 'filter' applied to digital operations is a bit unfortunate.
>> > An optical filter removes light according to its specification.  A
>> > digital, so called, filter does nothing of the sort.  It processes
>> > pixels according to the values of other pixels.  Deconvolution does
>> > EXACTLY the same thing - just with a more sophisticated algorithm.
>> > Fundamentally there is no difference.  I really wish the term 'filter'
>> > had never been used in the digital world.
>>
>> I still like to call it a "filter", and here is why: in digital
>> images, we do not have photons, but we have information. Information
>> is measured as entropy (the unit is "bits"). And no digital filter can
>> increase the information. They can at most retain the same amount of
>> information. But mostly they reduce information.
>>
>> So what about your deconvolution example?
>>
>> Let's go back first to the term "information" as per information theory.
>> The amount of information in something like an image can be described
>> as the average number of yes/no questions that have to be asked (given
>> optimally efficient questioning) to describe it fully.
>>
>> Of course, this implies that we *already* know something, e.g. that it
>> is a collection of pixels, in a certain geometric arrangement, the
>> pixel values are in a certain range, etc. Without such a context, the
>> information would be infinite and we would not be able to store it in
>> a file.
>>
>> With deconvolution, we basically use additional knowledge about the
>> image that is based on our assumption that the image formation
>> happened a certain way, with a given point spread function. It is
>> crucial to keep in mind that we reduce the amount of information in
>> the original image using the knowledge about how the experiment works
>> physically. It is even possible to put that information reduction into
>> laymen's terms: we strip away the information about what the camera
>> saw and retain only the information about the structures that gave rise
>> to the acquired image.
>>
>> Sure, you could regenerate that image, but again you would need to use
>> the knowledge about the optics; without that knowledge, the
>> information is no longer in the deconvolved image. (And even with the
>> knowledge, the reconstruction would be imperfect due to boundary
>> effects, but that's beside the point.)
>>
>> Keep in mind that information always lives in a context. If you knew
>> nothing about the bytes that make up this email, there would be no way
>> to compress it. But since you know that it is written in English,
>> using the ASCII encoding, you could compress it rather well. Even if
>> you knew only that a human wrote it using a common computer, you could
>> exploit the common knowledge that language is highly redundant, and
>> compress it e.g.
>> into a .zip file. (I like the compression example because it explains
>> the unit "bits" and it illustrates the need for a context: .zip files
>> compress rather poorly because the context "contains redundant and
>> repetitive byte sequences" does not apply.)
>>
>> The same is happening with deconvolution: you have the context that
>> you know a lot about the physics of image formation, and only that
>> allows you to strip away the blurriness. Now, from the point of view
>> of information theory, you strip away information. Which is good,
>> because it is (mostly) information you do not care about.
>>
>> With this reasoning in mind, I hope that it is less offensive that I
>> like the term "filter" in digital image processing.
>>
>> Ciao,
>> Johannes
>>
>