Compressed Sensing: Matching Pursuit

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EngWiPy
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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
 
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