# Compressed sensing

1. Apr 16, 2015

### maNoFchangE

I finally got a problem in my reading, so my problem is I am given a matrix $A$, column vector $f$, and a relation $f = Ag$ where $g$ is a column vector. The dimensions of those vectors and matrices are such that the above matrix multiplication makes sense, that is $A$ is not necessarily square. My goal is to compute $g$ but the number of rows of $A$ is less than the number of columns so that the solution is not unique. However the sought solution is required to be minimum in its $l_1$ norm, where $l_1$ norm of $g$ is defined to be $||g||_1 = \Sigma_i^N |g_i|$, I guess some of you are familiar with this norm type from linear algebra.
The above problem is clearly an optimization problem, but as I know there are few types of optimization problem, so if you had recongnized such a problem can you tell me what type of optimization my problem belongs to? So that I can navigate directly to the right chapter in my textbooks.

2. Apr 21, 2015