Re: [Eidors Help] document on inv_solve_abs_CG_logc

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Hi Andy,

I will see if I can fix it.

Best regards
Lakshmi.

On Tue, Oct 15, 2013 at 3:49 PM, Andy Adler <ad...@sc...> wrote:

> Hi Nolwenn, Hi Lakshmi,
>
> I would really like to see this function cleaned up, and made available as
> a tutorial. It gives another way to approach absolute imaging, and may
> be more stable in many cases.
>
> I just tried the UNIT_TEST, and the function isn't working (but it used
> to).
> Could you please try it, Nolwenn, and see if there is an obvious fix.
> >> inv_solve_abs_CG_logc UNIT_TEST
>
> Thanks
> --
> Andy Adler <ad...@sc...> +1-613-520-2600x8785
>
>
> On 15 October 2013 03:21,  <les...@sc...> wrote:
> > Dear Lakshmi,
> >
> > To choose the singular truncation value (later stored in the variable
> > tol), I wrote the equation using the Hansen 1999 paper
> > (
> http://www.sintef.no/upload/IKT/9011/SimOslo/vskoler/2005/notes/Lcurve.pdf
> ).
> > You'll find the equations 8 and 9 that describe XL2 and RES2.
> > Indeed I compute the tol value only for the first iteration of my
> > inversion and then I keep the same tol value.
> > My tol value is not automatically determined with this function, since
> you
> > first need to explore the best interval of the Lambda values that will
> > draw you an L that may not arise depending on your data quality, see:
> > Mamatjan, Y., Borsic, A., Gürsoy, D., & Adler, A. (2013). An experimental
> > clinical evaluation of EIT imaging with &#8467;1 data and image norms.
> > Physiological measurement, 34(9), 1027.
> >
> > What I usually do is: I run once the inversion with a large interval of
> > lambda values (stored in imdl.parameters.lambda) and plot the L-curve.
> > Then I run the inversion a second time with a lambda interval restricted
> > to the region close to the L-curve I plot again the L-curve for choosing
> > my tolerance value (on the corner of the L-curve or slightly on its right
> > to increase the filter strength) and then I write it into :
> > imdl.parameters.tol
> >
> > Since the problem may be non linear, I ran the inversion with something
> > like 10 iterations, with different imdl.parameters.tol values around the
> > one that seemed to be the best and I redraw an L-curve with the different
> > norm of the residuals I found at the end of my inversions and the norm of
> > the images roughness. I also compare the different resulting images, the
> > presence of artifacts on the images... The choice of imdl.parameters.tol
> > is of great importance, it depends on the geometry of your studied
> object,
> > the data quantity and quality... I don't think there is a simple way for
> > determining its best value, the difficulty is the same for the
> > determination of the hyperparameter values for the Gauss-Newton
> > algorithms.
> >
> > Later in the code, the choice of imdl.parameters.perturb may require also
> > some exploration...
> >
> > I hope that this could help you...
> >
> > Best regards,
> >
> > Nolwenn.
> >
> >
> >
> >> Hi Andy,
> >> The version I am using is eidors v3.7.1.  This is the file I found
> > online
> >> and you can see a function
> >> function tol= svdAnalysisLcurvecrit(data,img,J)
> >> <
> http://eidors3d.sourceforge.net/doc/eidors/solvers/inverse/inv_solve_abs_CG_logc.html#_subfunctions
> >
> > in line number 189. My questions relate to the definitions within this
> > function
> >> particularly from the line 206-217.  It is not under the deprecated
> > folder and hence was wondering if this is not used at all for
> >> the reconstructions.
> >> Thanks.
> >> Best regards
> >> Lakshmi.
> >> On Fri, Oct 11, 2013 at 2:36 PM, Andy Adler <ad...@sc...>
> > wrote:
> >>> Hi Lakshmi,
> >>> We may be looking at a different file. The most recent version is in
> > the
> >>> web link I gave you, and doesn't have those lines.
> >>> What version of EIDORS do you have? And what is the path to the file?
> --
> >>> Andy Adler <ad...@sc...> +1-613-520-2600x8785
> >>> On 11 October 2013 02:39, Lakshmi Selvakumaran
> >>> <lak...@ka...> wrote:
> >>> > HI Andy,
> >>> > The definitions are from the lines 206-217.  My question refers to
> > the
> >>> > definition of XL2 and RES2.
> >>> > Thanks.
> >>> > Best regards
> >>> > Lakshmi.
> >>> > On Fri, Oct 11, 2013 at 3:41 AM, Andy Adler <ad...@sc...>
> >>> wrote:
> >>> >> Hi Lakshmi,
> >>> >> The most recent version of the code is here:
> >>> >> http://sourceforge.
> >>>
> .net/p/eidors3d/code/HEAD/tree/trunk/eidors/solvers/inverse/inv_solve_abs_GN_logC.m
> >>> >> I'm having a little trouble seeing exactly where you have
> >>> >> the question. Can you point out the line numbers and code?
> >>> >> For example, we don't use variables with names beta or XL2.
> >>> >> --
> >>> >> Andy Adler <ad...@sc...> +1-613-520-2600x8785
> >>> >> On 9 October 2013 10:07, Lakshmi Selvakumaran
> >>> >> <lak...@ka...> wrote:
> >>> >> > Hello,
> >>> >> > Is there a reference that discusses the algorithm used in the
> >>> function
> >>> >> > 'inv_solve_abs_CG_logc'?
> >>> >> > There are some things that I don't understand completely.  If
> >>> anyone
> >>> can
> >>> >> > explain, it will be of great help.
> >>> >> > 1) In the SVD analysis, for the calculation of the XL2 variable,
> > it
> >>> is
> >>> >> > not
> >>> >> > multiplied by the right singular matrix, V.  In literature, the x
> >>> vector
> >>> >> > is
> >>> >> > the filter factor *( beta/singular values ) * vi.  But in the
> >>> function,
> >>> >> > the
> >>> >> > singular vectors vi is missing.  Why?
> >>> >> > 2) How is RES2 calculated?  Again, it seems to me that some terms
> >>> are
> >>> >> > missing.
> >>> >> > 3) Is the tol value that is calculated from the svd analysis
> >>> represent
> >>> >> > the
> >>> >> > level of truncation in the singular values?
> >>> >> > Thanks.
> >>> >> > Best regards
> >>> >> > Lakshmi.
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