Compressed Sensing: Matching Pursuit

[EngWiPy]

Hi,

I need a geometric explanation for this algorithm: Suppose we have the system Ax=b, where A is and M-by-N matrix, x is N-dimensional s(<<N)-sparse vector, and b is M-dimensional vector. There is an algorithm called Matching Pursuit to solve the above system efficiently:

1- Find the column of A that best match b.
2- The projection of b along that direction is removed and an updated b is obtained.
3- Repeat 1 and 2 until some termination criterion is met.

How these 3 steps solve the above system of linear equations?

Thanks in advance

 

[fresh_42]

I think it is better explained here:
https://en.wikipedia.org/wiki/Matching_pursuit
and here:
https://angms.science/doc/RM/OMP.pdf