How to use regularization with lsqnonlin function

10 次查看（过去 30 天）

显示更早的评论

AD 2020-11-14

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/648078-how-to-use-regularization-with-lsqnonlin-function

编辑： AD 2020-11-15

采纳的回答： Bruno Luong

在 MATLAB Online 中打开

Hi,

I would like to use lsqnonlin functinon with regularization (e.g. Tikhonov regularization). However, to my big surprise there is no such option it seems!

I like lsqnonlin because I can specify a cost function with an anonymous function in a convenient way.

Please, tell me there is a way to add regularization or another function that does the same thing with regularization?

Also please note that my fonction takes as input a matrix and convolves with a small kernel k:

fun = @(x)conv2(x,k,'same')-y;
lsqnonlinoptions=optimset('Algorithm','Levenberg-Marquardt','MaxIter',maxIterArg);
x_lsq =lsqnonlin(fun,x0,[],[],lsqnonlinoptions);

采纳的回答

Bruno Luong 2020-11-14

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/648078-how-to-use-regularization-with-lsqnonlin-function#answer_544768

编辑：Bruno Luong 2020-11-14

在 MATLAB Online 中打开

You are free to incorporation anything in the objective function, e.g., l^2 regularization

regcoef = some_small_coef;
fun = @(x) [reshape(conv2(x,k,'same')-y,[],1); regcoef*x(:)];

12 个评论
显示 10更早的评论隐藏 10更早的评论

AD 2020-11-15

编辑：AD 2020-11-15

在 MATLAB Online 中打开

Also I noticed lsqnonlin works with the conv2 problem I showed in the OP, but when I try:

fun = @(theta) reshape(imrotate(x,theta,'crop')-y,[],1);

it doesnt find the rotation angle and seem to just output the same x as I gave him (with very minor rotation maybe 1.5 degrees whereas I gave an y with 20 degrees) . Note that x is the ground truth image (no rotation) and y is the image with rotation see full code below)

any idea why it does not work with rotation? (Although I know there are other methods for estimating params but I am curious about lsqnonlin )

full function code so you can try it yourself:

function lsq_rec_estimRot_withReg(x,y,maxIterArg)
fun = @(theta) reshape(imrotate(x,theta,'crop')-y,[],1);
 
theta0 = randn();%initial guess
lsqnonlinoptions=optimset('Algorithm','Levenberg-Marquardt','MaxIter',maxIterArg);
theta_hat =lsqnonlin(fun,theta0,[],[],lsqnonlinoptions);
%% disp inside func for now
figure;
subplot(131);
imshow(x);
title('x');
subplot(132);
imshow(y);
title('y');
subplot(133);
imshow(imrotate(x,theta_hat,'crop'));
title(['x_{hat}, rot angle:' num2str(theta_hat) ] );
end

Bruno Luong 2020-11-15

I have no image-processing tbox so I can't try, and I guess I know the reason. But I stop to answer your many questions that drift from the original question.

AD 2020-11-15

编辑：AD 2020-11-15

Ok, - sorry for the many questions, its just that I am trying things - shall I post another question with this? It's just for getting a better intuition of things... I know there are algorithms for image re-alignment.

请先登录，再进行评论。

类别

MATLAB Mathematics Interpolation Interpolation of 2-D Selections in 3-D Grids

在 Help Center 和 File Exchange 中查找有关 Interpolation of 2-D Selections in 3-D Grids 的更多信息

产品

MATLAB

版本

R2020a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by

How to use regularization with lsqnonlin function

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

12 个评论
显示 10更早的评论隐藏 10更早的评论

更多回答（0 个）

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

How to use regularization with lsqnonlin function

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

12 个评论 显示 10更早的评论隐藏 10更早的评论

更多回答（0 个）

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

12 个评论
显示 10更早的评论隐藏 10更早的评论