I need to apply constrain using least square non negative function in Matlab

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sanjay 2024-9-6

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评论： sanjay 2024-9-13

Hi , I am working on Tikhonov Regularization and trying to reconstruct the absorption densities of experimental data using least square non negative function in matlab which takes my sensitivity matrix and measured data and solves for X unkonwn values, Now i want to apply constrain that during fitting it check whether my reconstruction is greater than or equal minimum values i assign manually and less than equal to maximum value is assign manually, the problem is lsqnoeng does not support upper bound and lower bound , can some one give me an idea how cani apply my constrain using lsnoneg

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回答（1 个）

Matt J 2024-9-6

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Use lsqlin instead.

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sanjay 2024-9-9

smoothening = Smoothening_roi(number_of_pixels);

max_L = max(abs(smoothening(:)));

smoothening = smoothening/max_L;

Null_matrix=zeros(number_of_pixels,1);

Tikh_Input.Integrated_Absorption_Line_1=IA.Integrated_Absorbance_per_pixel_line_1;

Tikh_Input.Integrated_Absorption_Line_2=IA.Integrated_Absorbance_per_pixel_line_2;

lambda_Tikh =1;

lambda_Tikh_2 =1;

Combined_Coeff_Matrix=[Coeff_Matrix_sparse ; lambda_Tikh.*smoothening];

Combined_Coeff_Matrix_2=[Coeff_Matrix_sparse ; lambda_Tikh_2.*smoothening];

Tikh_Input.Integrated_Absorption_Line_1 = IA.Integrated_Absorbance_per_pixel_line_1; % Line 1

Tikh_Input.Integrated_Absorption_Line_2 =IA.Integrated_Absorbance_per_pixel_line_2; % Line 2

Combined_projection_line_1=[Tikh_Input.Integrated_Absorption_Line_1;Null_matrix];

Combined_projection_line_2=[Tikh_Input.Integrated_Absorption_Line_2;Null_matrix];

lb1 = zeros(1601,1);

ub1=[];

lb2 =zeros(1601,1);

ub2=[];

z =lsqlin(Combined_Coeff_Matrix, Combined_projection_line_1, [], [], [], [], lb2, ub2);

y= lsqlin(Combined_Coeff_Matrix, Combined_projection_line_2, [], [], [], [], lb1, ub1);

Torsten 2024-9-9

编辑：Torsten 2024-9-9

We are unable to run this code because variables are undefined.

sanjay 2024-9-13

Okay i successfully reconstructed the results, but the probelm is when i directly use my data in AX =b form to reconstruct X , b is my data , then lsqlin doesnt reconstruct well. but when i scaled the data with maximum value in the data , by dividing this maximum value with data, also dividing this maximum value with upper and lower bound then it gives me good results and then i rescaled it by multiplying it with same maximum value ,Now i have concern why it is working good with scaled data and getting results with scaled data would be appropriate or not

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