Linear unmixing means to solve a set of linear equations to get the proportions of basic elements in the final composit. It is a linear mixture. If we have $f$ features and $m$ basic elements: \begin{equation} Y_{f\times 1} = M_{f\times m}F_{m\times 1}+\epsilon_{f\times 1} \end{equation}
where $Y$ is the estimated linear mixture vector, $M$ is the matrix of basic elements, and $\epsilon$ is the error.
This is like a linear regression or ordinary least squares and has closed form solutions. The problem is the above is just for one pixel, my question is can we do linear unmixing for a list of pixels in one shot? Instead of rerunning the above for each?
For example if we want to do above for $n$ data points one might model it like:
\begin{equation} Y_{f\times n } = M_{f\times m}F_{m\times n}+\epsilon_{f\times n} \end{equation}
I am not sure how to solve above equation in closed form (in one shot).