[X] My Assistant

[Harry]

The following images are for Tempel 1 originally taken by NASA's probe (left) and its de-convoluted image (right). For details of the technique used for that de-convolution, please visit;

http://139.134.5.123/tiddler2/c22508/focus.htm

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[Harry]

"The image of Metis, I can believe those are mostly real details that are bing enhanced. for Mira, my image-processing-instincts say mostly not."

The image of Mira may be just in focus. My software seems not work well when the original image has poor resolutions.

"So let's *test* the process with some known targets!"

Sorry, for I could not find appropriate example so far...

The following images are for Epimetheus taken by Cassini (left) and its de-convoluted image (middle / software: Focus Corrector, focus depth:= 1.8, iterations:= 8). As the reference I attached another image of Epimetheus taken at the position closer to the surface (right).

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[Harry]

The image of Vesta taken by HST (left) and its de-convoluted image (right) processed by Focus Corrector (focus depth:=4, iterations:=9)

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[Harry]

The image of Comet 73P/Schwassmann-Wachmann 3 (fragment "B") taken by HST (left) and its de-convoluted image (right) processed by Focus Corrector (focus depth:=2, iterations:=8)

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[Guest_DonPMitchell_*]

Not to keep nit picking, but "deconvolve" does not mean "sharpen", it is something different from what your program is doing.

In Fourier-transform space, convolution is equivalent to multiplying the image spectrum by a function f. Deconvolution tries to undo this by multiplying the spectrum by 1/f. It's a risky operation, because it can amplify noise. Norbert Wiener derived an optimal filter to bring out the most information given a certain noise level, called a Wiener filter, basically multiplication by 1/(f + c) for a magic value of c. Anyway, it is not just a sharpening kernel.

Photoshop CS2 has a filter called "Smart Sharpen", which I believe is true deconvolution. It seems to do an amazing job once you learn how to fiddle its parameters.

[Guest_DonPMitchell_*]

The following images are for Tempel 1 originally taken by NASA's probe (left) and its de-convoluted image (right). For details of the technique used for that de-convolution, please visit;

http://139.134.5.123/tiddler2/c22508/focus.htm

This got me curious, so I fiddled with this image of Tempel. First, fetch the original TIFF (not JPG) image from NASA. Note that it is 250 x 250 pixels, so undo their pixel-replication by resixing it from 500 to 250 with a "nearest-pixel" option in Photoshop. If you don't do that, all bets are off!

Then I ran it though Smart Sharpen deconvolution, with a radius of 1.5. More than that and the image rings, which indicates you made the radius too big. Here is the original and the deconvolved images, expanded again to 500 with a windowed sinc filter:

[attachment=5837:attachment]

I think the deconconved image is quite a bit cleaner than the sharpened image, although that may have jpeg artifacts amplified, or perhaps it was not downsized to 250 first?

[Bob Shaw]

Don:

Very nice! The 'new' detail is indeed very credible...

Bob Shaw

[Guest_DonPMitchell_*]

Don:

Very nice! The 'new' detail is indeed very credible...

Bob Shaw

In the technical papers about this camera system, there will probably be (should be!) a measurement of the aperture (convolution blur) function of the camera. So ideally, you would try to invert that.

Detail is revealed by amplifying higher frequencies, but this also amplifies the noise in the image, so you have to take care or you end up finding UFO bases in NASA photos (a favorite pass time for some folks)!

[Comga]

In the technical papers about this camera system, there will probably be (should be!) a measurement of the aperture (convolution blur) function of the camera. So ideally, you would try to invert that.

Indeed, the Deep Impact team has many star images to use as PSF models for deconvolution. They have this for the monochromatic images and through each filter. They also have computer models of the optical system which accuratly mimic the condition of the mirrors. With these, the don't need to do a "blind" sharpening but can do a true deconvolution, using one of several algorithms.

[Harry]

Not to keep nit picking, but "deconvolve" does not mean "sharpen", it is something different from what your program is doing.

In Fourier-transform space, convolution is equivalent to multiplying the image spectrum by a function f.

My method is different from Fourier transform. As you know, the output image g(x) is expressed as,

g(x) = f*n(x)

where the extent of n(x) corresponds to the deviation from the focal point (if g(x) is just in focus, then n(x) = ((delta))(x).) After applying Fourier transform to the above equation, we get;

G(u) = F(u)N(u)

hence,

F(u) = G(u)/N(u)

Therefore, by applying inverse Fourier transform to G(u)/N(u), we can get the image data f(x) before convolution. While my method is to solve the first equation: g(x) = f*n(x) directly. Firstly that equation is discretized as,

g(j) = ((sigma))_k f(j-k)n(k)

It is expressed with matrix-vector form as,

g = Af

hence,

f = A^(-1)g

The problem is how to calculate f(x) from the above equation. You may imagine to apply Gauss-Seidel method for it. But it can not be applicable in this case because A doesn't satisfy the condition in which the iteration by Gauss-Seidel method converges. Regarding the method I took, please refer to: http://139.134.5.123/tiddler2/c22508/iteration.htm

The attached images are the comparison of the original image (left)/the image you've got by Photoshop (middle-left)/the image obtained by Focus Corrector (middle-right)/another genuine image taken at the position closer to the surface of Tempel 1 (right). The parameters of Focus Corrector used for that image are:

Focus Depth = 1.7
Iterations = 7

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[Harry]

The image of Supernova 1987A taken by HST (left) and its de-convoluted image (right) processed by Focus Corrector (focus depth:=1.7, iterations:=7)

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