[scikit-image] Image deconvolution ...

[Juan Nunez-Iglesias]

Hi Jérôme,

Sounds great! I’ll admit that I’m not confident in this area either, but my reading of the documentation suggests that this is the right approach: the damping controls the square norm of x. By keeping it small (with large damping), you force the elements to be non-negative.

I hope the final picture looks good now! =) If you get a nice result, I suggest you write a blog post about it, with pictures. It sounds like a very cool use of SciPy, and would be a valuable addition to writeups about it!

Juan.

On 22 Nov 2017, 7:16 PM +1100, Jerome Kieffer <google at terre-adelie.org>, wrote:
> On Wed, 22 Nov 2017 12:40:50 +1100
> Juan Nunez-Iglesias <jni.soma at gmail.com> wrote:
>
> > Hi Jérôme,
> >
> > Can you explain your problem more? You know A and x and want to find
> > b? Is this an exact solution, or is Ax = b + err? SciPy’s
> > sparse.linalg module is where you’ll find most of your answers, I
> > think… If you want to *build* A from some description, you might find
> > our homography example in Elegant SciPy useful:
>
>
> Hi Juan,
>
> Thanks for your help. Nice documentation on scipy.sparse I wish I had
> it a couple of days ago.
>
> Indeed I have spent a week in building the matrix
> A using ray-tracing and now I believe it is almost correct now.
>
> The idea is to consider some image sensor (in 2D) which absorb the
> photon (X-ray) in volume (instead of the surface). So each pixel is considered
> as a voxel and the sensor is a 2D array of voxels.
> After this raytracing step, I know how much of a photon arriving in one
> pixel contributes to the neighboring pixels, this is my matrix A,
> (in CSR format).
>
> "b" is of course the image I read from the detector, with all element
> positive and I expect "x" to have all element positive as well.
>
> I tried to search in scipy.sparse.linalg the method which would allow
> me to retrieve "x" from "b". For now, the best I found is :
>
> res = linalg.lsmr(A, b, damp=damp, x0=b)
>
> When the damping factor is null or too small, I notice many wiggles
> (with negative regions) near peaks. For now I try to adjust this damp factor
> so that the minimum of x is positive but I am not confident on the
> method.
>
> --
> Jérôme Kieffer
> tel +33 476 882 445
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