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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
>