Abstract
The minimum-norm least-squares solution of the phase-closure equations of an interferometric array is very stable. Furthermore, this canonical solution can be obtained by simple backprojection, each closure phase leaving its “algebraic” imprint on the corresponding baselines. More precisely, the generalized inverse of the phase-closure operator C of an n-point array is equal to its adjoint (its Hermitian transpose) divided by n: C + =C * /n. Likewise, the generalized inverse of the phase-aberration operator B is equal to B * /n. These remarkable properties, which have so far remained unnoticed, play an essential part in the algebraic analysis of phase-closure imaging, and thereby in the understanding and the treatment of the inverse problems of aperture synthesis.
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