doi:10.1093/mnras/stt1994
ISI:000329158900003
AurĂa Rasclosa, Anna
Carrillo, Rafael
Thiran, Jean-Philippe
Wiaux, Yves
Tensor optimisation for optical-interferometric imaging
Oxford, Oxford Univ Press
http://infoscience.epfl.ch/record/187347/files/to4oi_mnras.pdf
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.
2013-06-28T14:30:54Z
http://infoscience.epfl.ch/record/187347
http://infoscience.epfl.ch/record/187347
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