  Fourier decomposition is a well established technique used in stellar
pulsation. However the quality of reconstructed light curves using this method
is reduced when the observed data have uneven phase coverage. We use simulated
annealing techniques together with Fourier decomposition to improve the quality
of the Fourier decomposition for many OGLE LMC fundamental mode Cepheids. This
method restricts the range that Fourier amplitudes can take. The ranges are
specified by well sampled Cepheids in the Galaxy and Magellanic Clouds.
  We also apply this method to reconstructing Cepheid light curves observed by
the HST. These typically consist of 12 V band and 4 I band points. We employ a
direct Fourier fit to the 12 V band points using the simulated annealing method
mentioned above and explicitly derive and use Fourier interrelations to
reconstruct the I band light curve. We discuss advantages and drawbacks of this
method when applied to HST Cepheid data over existing template methods.
Application of this method to reconstruct the light curves of Cepheids observed
in NGC 4258 shows that the derived Cepheid distance ($\mu_0=29.38\pm0.06$,
random error) is consistent with its geometrical distance
($\mu_0=29.28\pm0.09$) derived from observations of water maser.
