Re: PSF-based deconvolution

On Wed, 3 Aug 2005 03:05:31 +0200, "Bart van der Wolf"
<bvdwolf@xxxxxxx> wrote:

>> Are you still investigating PSF-based deconvolution?
>
>Yes, the status is as follows.
>
>Intro.
>It is preferable to use a slanted edge target, as the image of it will
>allow to produce an over-sampled edge profile (=Edge Spread Function
>or ESF). The first difference/derivative of that one dimensional ESF
>is called a Line Spread Function (LSF). An LSF is identical to a 1D
>integral of a 2D Point Spread Function (PSF).
>
>Since I have not found a (generally) simple to implement method of
>creating a 3D PSF out of a 2D LSF, I've taken the opposite approach.
>I've created a quick-and-dirty Excel Spread*** that builds a
>composite* Gaussian PSF, and then takes an approximate 1D integral of
>it, thus producing its LSF.
>This is then compared to the actual edge's LSF (calculated from the
>copy&pasted Imatest output), and by using the "Solver" add-in the
>squared error is minimized.
>
>* Composite meaning that I actually take multiple (currently 3)
>Gaussian PSFs with different Standard Deviations and weights (which is
>a suggestion I found in an Italian paper). Other functions could be
>modeled, but Gaussians have several useful properties.

Wow!
I'm trying to digest what you wrote.
Let's see:
Since deriving the actual PSF from the measured LSFs has proven
difficult, you somehow extimate an hypothetical PSF, then derive the
resulting LSFs and compare them to the actual measured LSFs, by
meaning of least squares.
But how do you exploit the differences and correct the presumed PSF?

>> I've found a new way to implement a L-R type deconvolution,
>> maybe! Still in the very early phase of the study.
>
>Interesting, as it was one of my main concerns for sharing this info.
>The results of the approximated PSF can be used in a variety of
>programs that use built-in Deconvolution functions based on an input
>kernel, but probably only few of this group's audience will have
>access to such a program.

I'm looking at an iterative approach.
A spatial-based iterative convolution with 2 different kernels is
performed on the soruce image. At each pass, an error indicator is
evaluated. When the difference between 2 consecutive passes is low
enough, the algorythm stops.

>Therefore, I've recently also added to my spread*** a High-Pass
>filter kernel generator that does a similar Job, but much faster.

But this way, you won't exploit the benefits of non-Gaussian PSFs.
While with true deconvolution, you may use non-symmetrical kernels,
multiple kernels, and so on. It should also help (by using
non-symmetrical kernels) reducing the effects of motion blur.
Right? Or am I missing something?

>The main difference between e.g. adaptive RL restoration and High-Pass
>filtering is that RL restoration will allow to extract a bit more info
>with better S/N ratio, but at the cost of a *much* longer processing
>time.

Very true. I briefly had a look at MMX instructions to see if I could
use them, but they are quite intricate and not generic enough (meaning
they depend on the compiler etc.).
Still, I'd happily let my 2.3 GHz Barton take care of the task:
sharpening before printing while I surf the web. :))))

>P.S. If your email address is valid, I could send you a copy of my
>(beta version) spread*** for evaluation.

The email address I use here is suffucated by an enormous amount of
spam unfortunately.
But if you swap the domain with "libero dot it" (same username), the
resulting address is valid. :)

Thanks!

Fernando
.