Tensor optimisation for optical-interferometric imaging

Abstract

Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We reformulate this nonlin- ear problem as a linear problem for the supersymmetric rank-1 order-3 tensor formed by the tensor product of the vector representing the image under scrutiny with itself. On one hand, we propose a linear convex approach for tensor recovery with built-in supersymmetry, and regularising the inverse problem through a nuclear norm relaxation of a low-rank constraint. On the other hand, we also study a nonlinear nonconvex approach with built-in rank-1 con- straint but where supersymmetry is relaxed, formulating the problem for the tensor product of 3 vectors. In this second approach, only linear convex minimisation subproblems are how- ever solved, alternately and iteratively for the 3 vectors. We provide a comparative analysis of these two novel approaches through numerical simulations on small-size images.

7 pages, 6 figures. Accepted in MNRAS

References in corpus (5)

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Cited by in corpus (5)

• Stable, Robust and Super Fast Reconstruction of Tensors Using Multi-Way Projections
• Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging
• Multi-target Detection with an Arbitrary Spacing Distribution
• A regularized tri-linear approach for optical interferometric imaging
• Large Scale 3D Image Reconstruction in Optical Interferometry