how to deconvolute a matrix?

hy guys,

i would like to deconvolute a matrix but i didn't find a 2d deconvolution function , any idea how to do that without using fft or ifft?

thank you in advance

code:

clear all
clc
a=randi(2,3)
b=randi(2,3)
c=conv2(a,b)
% [d,r]=deconv2(c,a)  this is what i would like to get
subplot(221)
img(a)
subplot(222)
img(b)
subplot(223)
img(c)
subplot(224)
img(d)

Answer 1

[Matt J]

Using

https://www.mathworks.com/matlabcentral/fileexchange/44669-func2mat-convert-linear-function-to-matrix

a=randi(2,3);
b=randi(2,3)

b = 3×3

2 1 2 2 2 1 2 1 1

c=conv2(a,b);

M=func2mat(@(x) conv2(a,x), zeros(3));

b_recon=reshape(M\c(:), 3,3)

b_recon = 3×3

2.0000 1.0000 2.0000 2.0000 2.0000 1.0000 2.0000 1.0000 1.0000

[Rabih Sokhen]

thank you alot !!!

[Rabih Sokhen]

hy Matt.

i still have one question plz.

suppose i have the following code

code:

clear all
clc
a=rand(10,3);
b=rand10,3);      %b=conv2(a,c)
%suppose that b is already the convolution of the array "a" with an   array "c"
% I would like to deconvulte " b " to re-obtain "a"  and  "c".
% usually "a" and "c" have the same size

M=func2mat(@(x) conv2(a,x), zeros(3));
c=reshape(M\b(:), 3,3);

subplot(131)
pcolora(a)
subplot(132)
pcolor(b)
subplot(1333)
pcolor(c)

% i obtained the followig erro :

Error using \

Matrix dimensions must agree.

Error in conv_et_deconv (line 69)

c=reshape(M\b(:), 3,3);

can you help me with this plz ?

[Matt J]

You are still using reshape() to create a 3x3 matrix, even though the result now has a different size.

[Rabih Sokhen]

Yes, I totally agree.

I'm stuck at this point and I didn't know how to solve it.

Can you tell me what to do or what to fix in the reshape to reobtain my array "a" and "c" plz ?

Thank you in advance

[Matt J]

If you have to ask, it means you haven't read the documentation for reshape(). Had you done so, you would find it really simple.

[Rabih Sokhen]

I have read the document

I know that's X=reshape (Z, n, m) will reshape the array Z into n*m array called X, also it should that n*m = number of elements of A

However the error in my code is in the division, in M\b(:). I never used sparse before and it looks that's the dimension of M does not agree with b to be able to to the division

hope I am not mistaken with the analyse

[Matt J]

Yes, you're right. An additional problem is that the 2nd input to func2mat() is also the wrong size .

m=10; n=3;  %expected dimensions of b

M=func2mat(@(x) conv2(a,x), zeros(m,n) );
c=reshape(M\b(:), m,n);

[Rabih Sokhen]

i did try it but i still have a error

code:

clear all

clc

a=rand(10,3);

b=rand(10,3);

[m,n]=size(a);

M=func2mat(@(x) conv2(a,x), zeros(m,n) );

c=reshape(M\b(:), m,n);

error

Error using \

Matrix dimensions must agree.

[Matt J]

a=rand(10,3);
b=rand(10,3)      

b = 10×3

0.7691 0.1625 0.7079 0.1838 0.4012 0.9035 0.2503 0.1830 0.4700 0.1909 0.4764 0.8176 0.2930 0.3865 0.2518 0.8353 0.4449 0.4590 0.1506 0.4136 0.5710 0.0331 0.2194 0.1108 0.3300 0.9208 0.1941 0.8414 0.2407 0.8796

c=conv2(a,b);
[m,n]=size(a);

M=func2mat(@(x) conv2(a,x), zeros(m,n) );
b=reshape(M\c(:), m,n)

b = 10×3

0.7691 0.1625 0.7079 0.1838 0.4012 0.9035 0.2503 0.1830 0.4700 0.1909 0.4764 0.8176 0.2930 0.3865 0.2518 0.8353 0.4449 0.4590 0.1506 0.4136 0.5710 0.0331 0.2194 0.1108 0.3300 0.9208 0.1941 0.8414 0.2407 0.8796

[Rabih Sokhen]

Hey Matt,

hope you are doing good today.

Thank you for your answer and I really appreciate your help.

concerning the code :

suppose that's i have "a" and "b"

a=rand(3,5)

b=rand(3,5)

and i am concidering that's b is already the 2d convloution of "a" with a array "c" and i don't have "c" .

how can i find "c" ?

thank you in advance

[Matt J]

For the matrix sizes you have shown, b cannot be the result of a convolution of a and another matrix c. The result of a convolution has to be larger than either a or c. In particular, it must satisfy

size(b)=size(a)+size(c)-1;

[Rabih Sokhen]

I have changed the size of the convolution array.

I considered nowthat "c" is the convolution array and the of size(c) =2*n-1 2*m-1 and c=conv2 (a, b)

Suppose I have "a" and "c"

I did deconvolute "c" with "a" to obtain "b" by using your method.

However, I tried to verify my answer by reconvoluting "b" with "a" and I expected to obtain "c", but I obtained a different result than "c"

did i wrote something wrong ?

thank you in advance

code:

clear all
clc
n=3;
m=5;

a=rand(n,m);

c=rand(2*n-1,2*m-1);  %c is already the convolution of a with b

M_a=func2mat(@(x) conv2(a,x), zeros(n,m));
b=reshape(M_a\c(:), n,m);

subplot(221)
img(a)
title('a')

subplot(222)
img(c)
title('c')

subplot(223)
img(b)
title('b=deconv2(c,a)')

subplot(224)
cc=conv2(b,a);
img(cc)
title('cc=conv2(b,a)')

[Matt J]

By generating c in a completely random manner c=rand(2*n-1,2*m-1), there is no gaurantee that it is the result of a convolution. The solution you are getting with M_a\c(:) is, however, the best estimate for b in the least squares sense.

[Rabih Sokhen]

I really appreciate your help.

Thanks you a lot

Answer 2

[Matt J]

I would like to deconvolute a matrix but i didn't find a 2d deconvolution function.

See deconvreg(), deconvlucy(), deconvblind(), and deconvwnr().

Answer 3

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/1620780-convolve-text-with-image#comment_1953810 shows an implementation for the case of it really only being 1d convolution

[Rabih Sokhen]

hy Walter , hope your doing well

I have seen your link, I don't have a strong background in Matlab, I have understood the global idea of it but not the entire script.

Matt already helped me alot and he did wrote me a great function, however i still have same error wen i try to deconvolute a array as in the folowing exemlple:

can you modify my code if that's possible?

code:

clear all
clc
a=rand(10,3);
b=rand(10,3);      
[m,n]=size(a);
M=func2mat(@(x) conv2(a,x), zeros(m,n) );
c=reshape(M\b(:), m,n);

error

Error using \

Matrix dimensions must agree.

[Walter Roberson]

That is Matt's code, not mine; explanation should come from him.