  The article undertakes the problem of pure state estimation from projective
measurements based on photon counting. Two generic frames for qubit tomography
are considered -- one composed of the elements of the SIC-POVM and the other
defined by the vectors from the mutually unbiased bases (MUBs). Both frames are
combined with the method of least squares in order to reconstruct a sample of
input qubits with imperfect measurements. The accuracy of each frame is
quantified by the average fidelity and purity. The efficiency of the frames is
compared and discussed. The method can be generalized to higher-dimensional
states and transferred to other fields where the problem of complex vectors
reconstruction appears.
