Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We review our previous work, which reformulates this nonlinear problem in the framework of tensor recovery and studies two different approaches to solve it: one is nonlinear and nonconvex while the other is linear and convex. We extend the linear convex procedure to account for signal sparsity and we also present numerical simulations that show the improvement in the quality of reconstruction of sparse images when including a sparsity prior.