  A new method of determining galaxy star-formation histories (SFHs) is
presented. Using the method, the feasibility of recovering SFHs with multi-band
photometry is investigated. The method divides a galaxy's history into discrete
time intervals and reconstructs the average rate of star formation in each
interval. This directly gives the total stellar mass. A simple linear inversion
solves the problem of finding the most likely discretised SFH for a given set
of galaxy parameters. It is shown how formulating the method within a Bayesian
framework lets the data simultaneously select the optimal regularisation
strength and the most appropriate number of discrete time intervals for the
reconstructed SFH. The method is demonstrated by applying it to mono-metallic
synthetic photometric catalogues created with different input SFHs, assessing
how the accuracy of the recovered SFHs and stellar masses depend on the
photometric passband set, signal-to-noise and redshift. The results show that
reconstruction of SFHs using multi-band photometry is possible, being able to
distinguish an early burst of star formation from a late one, provided an
appropriate passband set is used. Although the resolution of the recovered SFHs
is on average inferior compared to what can be achieved with spectroscopic
data, the multi-band approach can process a significantly larger number of
galaxies per unit exposure time.
