Sparsity regularized optical interferometric imaging

Optical interferometry involves acquisition of under-sampleddata related to the Fourier coefficients of the intensity image of interest,with missing phase information. It poses an ill-posed non-linear inverseproblem for image recovery. In this context, for monochromatic imaging,a tri-linear data model was proposed in [1], leading to a non-negative nonlinear least squares minimization problem, solved using a Gauss-Seidel method. In the recently submitted paper [2], we have developed a new robust method to improve upon the previous approach, by introducing as parsity prior, imposed either by an ℓ1 or a reweighted ℓ1 regularization term. The resulting problem is solved using an alternating forward backward algorithm, which is applicable to both smooth and non-smooth functions, and provides convergence guarantees in the non-convex context of interest. Moreover, our method presenting a general framework, we have extended it to hyperspectral imaging, where we have promoted a joint sparsity prior by an ℓ2,1 norm. Here we describe the proposed method and present simulation results to show its performance.