  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.
