Recall the measurement equation from last time:
Suppose again that the responses of the pixels to each light source are coherent. That is, we may hope that there is a basis 
such that the columns of 
are sparse. Then, we have that
or
That is, as long as 
‘s columns are sparse, we can infer it’s columns by working instead with the new measurements 
, which is basically 
projected into . One certainly hope that the columns of are even sparser than the columns of 
. If so, the number of measurements can be reduced greatly. However, I’m not so sure about this myself when it comes to wavelets, which is the basis I’m most likely to use.
Again, one can see that a big bottleneck in the above equation: to compute , we have to measure the color of every pixel of under every lighting condition used for measurement. And we know that measure the color of a pixel accurately takes a large number of rays. Actually, might be sparse in its rows. Can we acquire them with compressive sensing as well?
Notes 