pardon if this is in wrong cathegory, english is not my first language and I'm not that well aware of the english terms.

i.e. the classical g = M*f problem, where g is measured data and we want to know f.

In this case, with calibration data we can determine M, but it has an ill-conditioned inverse, so the classical solution of f = M

^{-1}*g doesn't work.

Enter the Tikhonov regularization, but it fails to be accurate enough.

Conjugate gradient method, i.e. solving min || M*f-g|| might work, if the M was positive definite, but it is not. (it's symmetrical though). Also, we demand that every element of f and g is either 0 or 1, as the measured data g is in binary form. Google scholar was of little help, so...

so in short

a) Is there any well know tools for the problem when the data is binaric

b) am I screwed?