Produce simple iradon geometry

Below I have a very basic script that creates a very small circular geometry when using the radon transform of my data. I have my "data =" defined as a few values that would be the values from one projection, I just want to take that projection and rotate it around 360 degrees such that it would produce a circle when I use the iradon() funciton. When I do this, it produces what I think I'd like, but it is so very small and pixelated. Is there a way to make the image larger? It looks like I took a CT scan of a tiny, dense, pea-sized object, but I would like it to appear on the screen as a dense torso-sized image. Any help would be great.

Thank you.

data = [0,1,2,3,4,3,2,1,0]
R1 = radon(data)

figure(1)
imagesc(R1)
colormap(hot)
colorbar

figure(2)
I1 = iradon(R1,0:179,'linear','none')
imshow(I1,[])

Answer 1

[Matt J]

data = [0,1,2,3,4,3,2,1,0];
theta=linspace(0,180,1000); theta(end)=[];
R1 = radon(data,theta);


figure(2)
N=numel(theta);
R2=repmat(R1(:,1),1,N);
for skip=[1000, 500, 250,125,60,1];
    nexttile
 I = iradon(R2(:,1:skip:end),theta(1:skip:end),'spline','none',1,30);
 imshow(I,[])
end

[Brett Ruben]

Any idea on how I might be able to use this for different data at different angles? In this example I used one data set from a single projection and just rotated that about the object. If I have an asymmetric object, I would need mutiple projection angles to resolve the image. So say I have 36 projection angles, one projection every 10 degrees, and an array of length 11 data points across that scan at each angle. How might I be able to back project this data?

With the example above it was just one array rotated about the object, what about for multiple arrays of data for each of the projection angles?

Thank you

[Matt J]

I don't think it should be any different.

Answer 2

[Voss]

Maybe use the optional input argument output_size when you call iradon:

data = [0,1,2,3,4,3,2,1,0];
R1 = radon(data);
figure(1)
imagesc(R1)
colormap(hot)
colorbar

figure(2)
I1 = iradon(R1,0:179,'linear','none',20)

I1 = 20×20

0.6340 0.6683 0.7031 0.7405 0.7747 0.8087 0.8361 0.8579 0.8734 0.8780 0.8734 0.8579 0.8361 0.8087 0.7747 0.7405 0.7031 0.6683 0.6340 0.5984 0.6684 0.7147 0.7574 0.8034 0.8481 0.8885 0.9290 0.9564 0.9784 0.9854 0.9784 0.9564 0.9290 0.8885 0.8481 0.8034 0.7574 0.7147 0.6684 0.6286 0.7077 0.7596 0.8176 0.8746 0.9345 0.9872 1.0400 1.0821 1.1098 1.1233 1.1098 1.0821 1.0400 0.9872 0.9345 0.8746 0.8176 0.7596 0.7077 0.6621 0.7484 0.8097 0.8782 0.9550 1.0358 1.1119 1.1786 1.2426 1.2830 1.3004 1.2830 1.2426 1.1786 1.1119 1.0358 0.9550 0.8782 0.8097 0.7484 0.6949 0.7909 0.8643 0.9468 1.0426 1.1497 1.2642 1.3633 1.4551 1.5222 1.5368 1.5222 1.4551 1.3633 1.2642 1.1497 1.0426 0.9468 0.8643 0.7909 0.7261 0.8308 0.9166 1.0202 1.1447 1.2869 1.4467 1.6071 1.7528 1.8613 1.8877 1.8613 1.7528 1.6071 1.4467 1.2869 1.1447 1.0202 0.9166 0.8308 0.7579 0.8649 0.9646 1.0894 1.2451 1.4487 1.6887 1.9540 2.1978 2.3562 2.4796 2.3562 2.1978 1.9540 1.6887 1.4487 1.2451 1.0894 0.9646 0.8649 0.7818 0.8940 1.0071 1.1506 1.3396 1.6019 1.9705 2.4682 2.9882 3.3692 3.4533 3.3692 2.9882 2.4682 1.9705 1.6019 1.3396 1.1506 1.0071 0.8940 0.8058 0.9195 1.0449 1.2082 1.4341 1.7776 2.3707 3.3750 4.5027 5.4460 5.7448 5.4460 4.5027 3.3750 2.3707 1.7776 1.4341 1.2082 1.0449 0.9195 0.8220 0.9125 1.0374 1.2071 1.4517 1.8499 2.6857 4.3333 6.3157 8.1873 9.8322 8.1873 6.3157 4.3333 2.6857 1.8499 1.4517 1.2071 1.0374 0.9125 0.8158

imshow(I1,[])

[Brett Ruben]

Thank you for your response. The problem is still here as far as the pixelation goes. I would like to create something like the attached image.

[Voss]

All I can suggest is to increase the output_size in iradon further, to reduce the appearance of pixelation.

data = [0,1,2,3,4,3,2,1,0];
R1 = radon(data);
figure(1)
imagesc(R1)
colormap(hot)
colorbar

figure(2)
I1 = iradon(R1,0:179,'linear','none',64);
imshow(I1,[])

I'm not sure what those 8 different images all are nor what the numbers (1,2,4,8,16,32,64,180) mean. If you want to reproduce those 8 images, it seems like you'll have to use something besides (or in addition to) iradon.