  In quantum state tomography, one potential source of error is uncontrolled
contact of the system with a heat bath whose detailed properties are not known,
and whose impact on the system moreover varies between different runs of the
experiment. Precisely these variations provide a handle for reconstructing the
system's effective relaxation dynamics. I propose a pertinent estimation scheme
which is based on a steepest-descent ansatz and maximum likelihood. After
reconstructing the relaxation dynamics, the original quantum state of the
system can be constrained to a curve in state space.
