# sensing and representation matrices from exhaustive data

If I know y (samples) and x (signal), is there a practical matlab algorithm to calculate A in y = Ax?

The solution is probably not unique.

$$\left[ { \begin{array}{cc} a & b \\ c & d \end{array} } \right] \left[{\begin{array}{c} 1 \\ 0 \end{array}} \right] = \left[{\begin{array}{c} 1 \\ 1 \end{array}} \right]$$

$b$ and $d$ can be any value provided $a = c = 1$

• @jonsca thank you very much for the math formatting ! – lennon310 Jan 6 '14 at 21:38
• You're welcome. The matrix syntax is a little cumbersome, but it makes a nice result. – jonsca Jan 6 '14 at 21:39

You could use tensor factorization methods. For example if you are sure that your data is non-negative, then Nonnegative Matrix Factorization might be used.

http://www.mathworks.com/help/stats/nnmf.html

Depending on your application and format of A, you might want the sparsest solution. In that case minimization of $L_0$ norms would be considerable.

• Interesting, thank you. The data is an image so they are all nonnegative values. I'm working with matrix completion algorithms but I first wanted to test an incoherence property - see dsp.stackexchange.com/q/13567/4038 – val Jan 6 '14 at 22:29