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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

Comments and Ratings (58)

gcv() function appears to produce a crude approximation of an optimal lambda. It chooses only 200 values of lambda and picks the minimum GCV value among the 200. When I compute the minimum GCV using fminbnd() I get a different lambda even-though the GCV value is the same in both methods. Did anyone test the accuracy of gcv() by other algorithms?

Hongkai Liu

irain sun

Excellent package,very Good!!Thanks!!

Franz Heuchel

Franz Heuchel

Why is there no python version?

Virinchi Roy


KUI DU (view profile)

Great tools!!!

Linh Dinh

Jinhui Zhang

yh tao

yh tao (view profile)


dhaba india


zhao (view profile)

Abir M

Abir M (view profile)

yogev gabay



cheung (view profile)

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


Andrea Libri

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.

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

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.

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?

Zhao wenming


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

Aslak Grinsted

Aslak Grinsted (view profile)

dennis gou

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

Ander Biguri

Ander Biguri (view profile)

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!!!!!

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!


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?



Feiyan (view profile)

Andrey Ivanov



Hong (view profile)


Oscar (view profile)

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


Piet (view profile)



ls (view profile)

good work

Martin Fuchs

Well written Code thanks to the Author


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

Xuecang zhang

thanks a lot ,very convenient and powerful
sharing is good

yuan qiangqiang

very good !

praveen kumar

These are really useful & essential programs.

leon button


sdfasf kjdlfkalsdj

abdel jardani


Ruslan Pechenkin

Thanks a lot, it is very useful

Nicolas MARIE

Thank you for this very useful package.

Valeriy Kruchko

Thank you for this job.

Dr.Feras AL-Faqih

Ben Fisher

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

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.

Volker Rath

Indispensable for everybody working on
inverse problems.

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.



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

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

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MATLAB 7.5 (R2007b)

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