Find pixel mapping matrix with minimum iterations The Situation
 I am an electronics engineer and on a volunteer team that have built a prototype eye that has 200*200 sensors that are mapped to the optic nerve, the connection to the optic nerve is random (organic connection is grown) so I need to have the patient draw what they see, I am trying to limit the number of drawings (difficult for a blind person) the patient has to do to get the relationship between the artificial eye output and the correct perception of the image.

The Problem
Given a input image/matrix and an viewable/readable output matrix, what is an algorithm to automatically identify the encoding  with the least number of iterations.



By changing the input one pixel at a time and then examining the output, the relationship can be discovered, this is, however, very inefficient.
Number the pixels from $0$ to $n^2-1$. Then create $\lceil \log_2n^2\rceil$ many pictures. In the $i$-th picture all pixels are black, if the $i$-th bit in their number is $1$, white otherwise.

Note: If you have $2^k$ colors available, you can choose the color for each pixel based on $k$ successive bits of the number. This will reduce the number of images by a factor of $k$.