
IPscatt---a MATLAB Toolbox for the Inverse Medium Problem in Scattering

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# Source Code Levels

The source code is classified into three source code levels:

* level 1: public (basic functions, described in [2] and [3], i.e. the reconstruction is restricted to the primal-dual algorithm)
* level 2: closed (features described in [4])
* level 3: intern (internal experiments)

The closed source code requires the public source code and the intern source code requires the closed source code.

The availability of the different source code levels depends on the release.

Releases:

* ipscatt2017 (level 1) (Copyright 2017; pulished December 2019) in [3]
* ipscatt2019 (level 2) (Copyright 2017, 2018; published December 2019) in [4]

To add the required pathes we have corresponding initialization levels in the routine init.

It follows a more detailed description of the source code levels.


# level 1: public source code of IPscatt

* Content: modules/function groups:
  - Initialization
  - Experimental Set-Up
  - Data Readers
  - Constrast Reconstrucion:
    The public source code is restricted to the reconstruction with a primal-dual algorithm (seti.invNo = 6).

* Publication: same parts of IPscatt as provided as supplementary material to [3].
               (Received October 2017; revised August 2018; revised April 2019; accepted April 2019; published December 2019)

* Documentation: detailed reference of all functions.

* Labeling: not specially marked (with a suffix).

* Remark: The user guide only refers to the public source code.


# level 2: closed source code of IPscatt

* Content (additionally):
  - heuristic algorithm for an automatic, data-driven parameter choice of the regularization parameters, see Sec. 3.3.3 in [4].
  - reconstruction method using the factorization method's result as described in Ch. 8 in [4].
  - two versions of the thresholded, nonlinear Landweber scheme:
    . based on the soft-shrinkage operator:
      the source code was adopted from sparseScatt, that is the MATLAB toolbox behind the numerical examples in [1].
    . based on the developed extended soft-shrinkage operator, mentioned in Sec. 3.3 and defined in (6.7) in the dissertation in 2019.
  - In addition it contains the using of wavelets (that was less successfull):
    . soft-shrinkage with wavelets, see Sec. 6.3 in [4].
    . reconstruction with a primal-dual algorithm using wavelets, see Sec. 7.7 in [4].

  For more information see [4]:
  - Ch. 1, Paragraph "Source Code Archeology".
  - Sec. 4.1, Paragraph "Public and Closed Source Code".

* Publication: provided as supplementary material to [4].
               (Submitted April 2019; published December 2019)

* Documentation: less detailed documentation.
  (e.g. additional predefined contrasts are not described in incontrastsRef.m)

* Labeling: suffixed with "Closed".

* Remark: partly not fully integrated.
  In particular, this concerns the factorization method and the heuristic algorithm for a choice of regularization parameters as they are not available via start. To use them, see addAutoparamClosed/autoparam3.m and addFactClosed/factorizationGuide.m.


# level 3: intern source code of IPscatt

* Content: internal experiments.
* Publication: not intended.
* Documentation: partly.
* Labeling: suffixed with "Intern".


# References

[1] Armin Lechleiter, Kamil S. Kazimierski, and Mirza Karamehmedovic. 
    Tikhonov regularization in $L^p$ applied to inverse medium scattering. 
    Inverse Problems, 29(7):075003, 2013.
    URL: https://doi.org/10.1088/0266-5611/29/7/075003.

[2] Florian B&uuml;rgel, Kamil S. Kazimierski, and Armin Lechleiter. 
    A sparsity regularization and total variation based computational framework for the inverse medium problem in scattering. 
    Journal of Computational Physics, 339:1-30, 2017. 
    URL: https://doi.org/10.1016/j.jcp.2017.03.011.

[3] Florian B&uuml;rgel, Kamil S. Kazimierski, and Armin Lechleiter. 
    Algorithm 1001: IPscatt---A MATLAB Toolbox for the Inverse Medium Problem in Scattering. 
    ACM Transactions on Mathematical Software, 45(4), Article 45, 20 pages, 2019. 
    URL: https://doi.org/10.1145/3328525.

[4] Florian B&uuml;rgel.
    Effective and Efficient Reconstruction Schemes for the Inverse Medium Problem in Scattering.
    PhD thesis, Universit&auml;t Bremen, 2019.

