How to convolve a 3D matrix along one of its dimension?

I have a 100by100by2000 ish matrix, say 3rd dimention is representing time where the 100*100 matrix changes. I wanted to convolve this whole matrix through a temporal gaussian filter along the 3rd dimention (the one that is 2000ish long).

With the code I know of I can only think of making a for-loop and do conv() 10000 times. (cuz I believe conv() can only operat on single dimention vectors?) However this for-loop will then be extremely long and it seems like it would take forever to run. I have attached a visual illustration of what I wanted to do.

So my question is: is there a function that is equivilent to conv() that can allow me to do this in more eifficient way? Or can I actually make conv() to run in a vectorized way?

I am aware that there is a fucntion called filter(), but I wasnt really sure what does that function do. If filter actually would work can anyone tell me what is the similarity and difference between filter and conv?

Thx a lot.

Answer 1

[Matt J]

If your Gaussian kernels is 1x1xN, you can just use convn as usual

kernel=reshape(gaussianProfile,1,1,[]);

output=convn(Array, kernel);

[Yuxin Tong]

Thx! I think this worked!

Answer 2

[Akira Agata]

The function smoothdata must be applicable, like:

% Sample data
A = rand(100, 100, 2000);

% Gaussian filter window
win = 15;

% Apply smoothdata along 3rd dimension
dim = 3;
A2 = smoothdata(A, dim, 'gaussian', win);

% Let's check!
figure
plot(squeeze(A(1, 1, :)),'c')
hold on
plot(squeeze(A2(1, 1, :)),'b')
legend({'Original', 'After filtering'})
title('Signal A(1,1,:)')

Answer 3

[Matt J]

You can use ffts

kernel=reshape(gaussianProfile,1,1,[]);

N=size(Array,3)+size(kernel,3)-1;

F=@(z)fft(z,N,3);
invF=@(z)ifft(z,[],3,'symmetric');

kernel=reshape(gaussianProfile,1,1,[]);

output = invF( F(kernel).*F(Array) );

Answer 4

[Matt J]

If you have the Image Processing Toolbox, you can use imgaussfilt3,

output = imgaussfilt3(Array,[.1,.1,sigma]);