Re: PSF-based deconvolution


"Fernando" <fcarello@xxxxxxxxxxxxx> wrote in message news:ep91g19na85msraq1bka3tb63us0jgtmij@xxxxxxxxxx
SNIP 
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.


Correct.

But how do you exploit the differences and correct the
presumed PSF?

The presumed PSF is generated in almost the same dimensions as the Imatest edge profile CSV output (I use -5.75 to +9.75 pixels in 0.25 steps due to differencing), and is based on 3 different Standard Deviations. So for all cells in a 63x63 quarter pixel square I calculate the combined amplitudes of (in my case) 3 Gaussian PSF distributions.

I then use Excel's Solver add-in to minimize the squared error between the LSF (1 dimensional integral of the presumed PSF) and the 1st difference of the edge profile. That doesn't take very long to calculate, in the order of just a couple of seconds depending on processing power.

In fact, I've been fiddling with the spread*** and have come up with an even more accurate variation on the same theme, I take the integral of the LSF and minimize the error with the original edge profile (that will accommodate to irregular/noisy edge profiles better).

Now I need to tidy up the spread*** a bit, to avoid whatever little human intervention is still needed after copy/paste of the Imatest data.

Currently the only human intervention needed, besides starting the Solver, is in setting the High-Pass filter kernel size, because that is also calculated (experimental feature, may need some more work), but once set it can be saved and forgotten.

<http://www.reindeergraphics.com/free.shtml#customfilter> allows to set a 7x7 pixel convolution kernel, which is better than Photoshop's 5x5, and it allows floating point input (copy from spread***, paste in e.g. notepad txt file).

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.

Sounds a bit like <http://www.ra-dec.de/bv/filter-la.html> where an intermediate image is convolved (? the author is not clear) with a convolution kernel and compared to the original. From the difference between them a new intermediate image is calculated, and so on for several iterations.

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?

You are right, but it depends on the goal one sets. My first goal was to reduce/compensate for the effect of the lens+AA-filter in DSLRs, and lens+film+scanner MTF losses (AKA capture sharpening). A benefit of Gaussians is that they are separable, i.e. the rows and columns can be convolved in two passes with a much smaller FIR filter. Also, the combination of several blur sources is often well approximated by a Gaussian.

There is no fundamental problem in generating non-Gaussian PSFs, it only complicates the calculations, and the application of them needs very large kernels to accommodate their shape. The same goes for HP-filters, they can be any shape.
I'm also looking into adding De-focus correction, the PSF of which resembles more that of a cylinder than of a Gaussian.

SNIP 
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. :)

Done. Let's discuss the spread*** details by email until we have something worth sharing with a larger group or with Norman Koren.

Bart 

.