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16 Apr 1998 (Updated )

Analysis and Solution of Discrete Ill-Posed Problems.

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Regularization Tools: A MATLAB package for Analysis and Solution of Discrete Ill-Posed Problems. Version 4.1.
By means of the routines in this package, the user can experiment with different regularization strategies. The package also includes 12 test problems.

Requires Matlab Version 7.3. The manual and more details can be found at


This file inspired Regularization Kaczmarz Tools Version 1.4 For Matlab, Three Dimensional Atmospheric Tomography Toy Model, and Nlc Smooth Reg.

MATLAB release MATLAB 7.5 (R2007b)
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Comments and Ratings (48)
16 Dec 2016 yh tao

yh tao (view profile)


09 Nov 2016 dhaba india

29 Sep 2016 zhao

zhao (view profile)

20 Sep 2016 Abir M

Abir M (view profile)

24 Aug 2016 Ridley Rebecca

06 May 2016 yogev gabay

25 Apr 2016 Craig1028

09 Mar 2016 cheung

cheung (view profile)

Excellent package. I love this package and it is perfect for me.

07 Mar 2016 s136620

14 Feb 2016 Andrea Libri

01 Feb 2016 Daniel Vasilaky

My Iterative Tikhonov performs a bit better than
the package's combo. l-curve(), Tikhonov()
Using A=Golub(12),x=ones(12,1), b=A*x, e=normrnd(0,.1,r,1), b=b+e; the package's relative error is 0.254 my algorithm's relative error 0.233. Iterative Tikhonov performs significantly better than Landweber and Kaczmarz in the package for all iterations.

Comment only
01 Feb 2016 Daniel Vasilaky

15 Jan 2016 Fernando Otero

Excellent package. I used it for my Ph.D. and now I'll try with the updated version. Thanks a lot. Just wondering if there is any open implementation of modified routines for some of the algoritms such as Robust GCV, The Robust GCV and the Trnasformed Discrepancy Principle

11 Sep 2015 Naima Naheed

I got the answer. My blurring matrix was incorrect. Only problem is that it is hard to work on MATLAB when the image size is 512 by 512. I hope that in the future MATLAB will take care of this issue.

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29 Aug 2015 Naima Naheed

I am concerned about tsvd.m
While I was using iogray.tif as an image file(P C Hansen suggested), MATLAB does not work. I don't know when it will work. Is there anyone in the world to help me?

Comment only
23 Jul 2015 Zhao wenming


Comment only
08 Apr 2015 vijay Bisalahalli

What are the input to tikhonov regularisation function.i mean tel me what are those u s v b x_0.reply me soon.

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16 Feb 2015 Aslak Grinsted

Aslak Grinsted (view profile)

11 Feb 2015 dennis gou

I want to find that which funtion is uesed to call the "art.m"? Is an test for "art.m" avaliable?

17 Nov 2014 Ander Biguri

Ander Biguri (view profile)

16 Apr 2014 Carlos Palma

Poorly documented. My own experience with it has been that I cannot know what matrices must I pass as arguments for these functions. For example when using l_corner I have found that you have to pass a matrix s, which I believe to be the matrix given by svd (nowhere it says whether this is right or wrong), and I always get an error because it tries to compute beta./s, with beta=U'*b, which in my case means beta is a 6x1 matrix, while s is a 6x6 matrix. How am I supposed to know how to solve this?, I'm just studying the basics of regularization!!!!!

09 Mar 2014 kaiba Wong

Very essential tools
I am trying the tikhonov function and getting errors...
suppose my Ax=b
A=matrix of 11375x3
b=vector of 11375x1
I calculated svd of A using svd(A,0)
assuming x_0 is zero
and insert lambda as [10,1,1e-2]
unfortunately..I keep getting an error that
Error in tikhonov (line 66)
if (nargin==6), omega = V\x_0; omega = omega(1:p); end

anyone having the same problem?...Thanks!

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13 Feb 2014 Thomas

Thomas (view profile)

Great package but, what is what...?

I have a data vector, and a model for calculating a theoretical data vector. What variables are the data vector and model in the call? Could someone lay out what each of these are?


29 Oct 2013 Feiyan

Feiyan (view profile)

13 Aug 2013 Andrey Ivanov

04 Jan 2013 Nikolai

22 Dec 2012 Charles Nelatury

25 Aug 2012 Hong

Hong (view profile)

29 Jun 2012 Oscar

Oscar (view profile)

22 Mar 2012 Christopher Coello

Great package, really useful to understand better resolution of ill-posed problems

23 Dec 2011 Piet

Piet (view profile)


16 Dec 2011 ls

ls (view profile)

good work

07 Dec 2011 Martin Fuchs

Well written Code thanks to the Author

15 Oct 2011 LucasCritique

Fantastic package! Easy to use, stable, great documentation. Many thanks to the author!

23 Oct 2008 Xuecang zhang

thanks a lot ,very convenient and powerful
sharing is good

01 Aug 2008 yuan qiangqiang

very good !

22 May 2008 praveen kumar

These are really useful & essential programs.

28 Jun 2007 leon button


10 Apr 2007 sdfasf kjdlfkalsdj

06 Mar 2007 abdel jardani


Comment only
23 Jul 2004 Ruslan Pechenkin

Thanks a lot, it is very useful

07 Mar 2004 Nicolas MARIE

Thank you for this very useful package.

03 Nov 2003 Valeriy Kruchko

Thank you for this job.

09 Apr 2003 Dr.Feras AL-Faqih

25 Jan 2002 Ben Fisher

Great collection of tools. It needs some time to get familiarised with all functions though the documentaion is good.

28 Nov 2001 Wlodek Tych

Excellent tool, good documentation. As with other powerful methods you have to know what you are doing.

Many thanks to the Author for writing and sharing.

21 Oct 2001 Volker Rath

Indispensable for everybody working on
inverse problems.

30 Sep 2001 Brian Borchers

This is a very useful package of tools for
the regularization of linear inverse problems. I've found this package to be very
useful both in research and in teaching a
course in inverse problems.

One minor complaint- the author
has released an updated version for MATLAB 6
which isn't on MATLAB Central yet.


modifying description

05 Dec 2002

Added screenshot

25 Feb 2008

New version for Matlab 7.3, with a number of buf fixes and new capabilities, publihsed in Numer. Algo. 46, pp 189

01 Feb 2015 1.1

Various small bugs are fixed, and the help lines are expanded a bit (for those that don't read manuals).

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