  With the availability of galaxy distance indicators in weak lensing surveys,
lensing tomography can be harnessed to constrain the three-dimensional (3D)
matter power spectrum over a range of redshift and physical scale. By combining
galaxy-galaxy lensing and galaxy clustering, this can be extended to probe the
3D galaxy-matter and galaxy-galaxy power spectrum or, alternatively, galaxy
biasing parameters. To achieve this aim, this paper introduces and discusses
minimum variance estimators and a more general Bayesian approach to
statistically invert a set of noisy tomography 2-point correlation functions,
measured within a confined opening angle. Both methods are constructed such
that they probe deviations of the power spectrum from a fiducial power
spectrum, thereby enabling both a direct comparison of theory and data, and in
principle the identification of the physical scale and redshift of deviations.
By devising a new Monte Carlo technique, we quantify the measurement noise in
the correlators for a fiducial survey, and test the performance of the
inversion techniques. We conclude that a shear tomography analysis of near
future weak lensing surveys promises fruitful insights into the effect of
baryons on the nonlinear matter power spectrum at z<~0.3 around k~2 h/Mpc, and
into galaxy biasing (z<~0.5). However, a proper treatment of anticipated
systematics -- not included in the mock analysis but discussed here -- is
likely to reduce the signal-to-noise in the analysis so that a robust
assessment of the 3D matter power spectrum probably asks for a survey area of
at least 1000 sdeg. [Abridged]
