Principles of Image Reconstruction in Interferometry

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Image reconstruction from interferometric data is an inverse problem. Owing to the sparse spatial frequency coverage of the data and to missing Fourier phase information, one has to take into account not only the data but also prior constraints. Image reconstruction then amounts to minimizing a joint criterion which is the sum of a likelihood term to enforce fidelity to the data and a regularization term to impose the priors. To implement strict constraints such as normalization and non-negativity, the minimization is performed on a feasible set. When the complex visibilities are available, image reconstruction is relatively easy as the joint criterion is convex and finding the solution is similar to a deconvolution problem. In optical interferometry, only the powerspectrum and the bispectrum can be measured and the joint criterion is highly multi-modal. The success of an image reconstruction algorithm then depends on the choice of the priors and on the ability of the optimization strategy to find a good solution among all the local minima.