  We present a new approach for image reconstruction and weak lensing
measurements with interferometers. Based on the shapelet formalism presented in
Refregier (2001), object images are decomposed into orthonormal Hermite basis
functions. The shapelet coefficients of a collection of sources are
simultaneously fit on the uv plane, the Fourier transform of the sky brightness
distribution observed by interferometers. The resulting chi-square fit is
linear in its parameters and can thus be performed efficiently by simple matrix
multiplications. We show how the complex effects of bandwidth smearing, time
averaging and non-coplanarity of the array can be easily and fully corrected
for in our method. Optimal image reconstruction, co-addition, astrometry, and
photometry can all be achieved using weighted sums of the derived coefficients.
As an example we consider the observing conditions of the FIRST radio survey
(Becker et al. 1995; White et al. 1997). We find that our method accurately
recovers the shapes of simulated images even for the sparse uv sampling of this
snapshot survey. Using one of the FIRST pointings, we find our method compares
well with CLEAN, the commonly used method for interferometric imaging. Our
method has the advantage of being linear in the fit parameters, of fitting all
sources simultaneously, and of providing the full covariance matrix of the
coefficients, which allows us to quantify the errors and cross-talk in image
shapes. It is therefore well-suited for quantitative shape measurements which
require high-precision. In particular, we show how our method can be combined
with the results of Refregier & Bacon (2001) to provide an accurate measurement
of weak lensing from interferometric data.
