[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

Attached thumbnail(s)

 

[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

Attached thumbnail(s)

 

[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)

Attached thumbnail(s)