Compressed Sensing

Computational Linear Algebra
1

I’m having trouble understanding what is going on in this algorithm. Can someone explain in plain English

  1. how we build the projection operator?
  2. what does Linear Algebra have to do this problem? My gloss from reading around on the web is that we are trying to solve a linear system of equations Ax = b where the system is underdetermined. I guess this is why we use the L1 minimization to find the best solution instead of least squares but I haven’t been able to find a good explanation for how this works. Could someone help me out with this?

Thanks.

2

Have you watched the beginning of video 8? I try to re-explain the compressed sensing problem there and I think I do a clearer job than in video 7.

A: is the projection matrix, based on the location and angles where the x-ray passes (for each of the k x-rays taken). These are unraveled to make a k by (l x l) matrix.

This is always the same and doesn’t depend on what is being x-rayed.

Each box below is flattened to be one row of the projection matrix:

image
image.png837×1247 50.4 KB

x: what we’re solving for, the thing being x-rayed
b: intensities measured by the x-ray passing through what is being x-rayed

1 Like
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Hi Rachel, First of all a big thanks for all the great content you have provided. I have this doubt in this topic that we are taking the proj_operator as X which is constant
and Predicting Y proj (in 1d as proj.ravel) so what is the input we are giving in this statement
`rec_l1 = rgr_lasso.coef_.reshape(l, l) I understand about X and Y for our inputs to Linear regression. But I am confused that for the final image generated it’s for what input?

`