Different versions of the cost function, J, which is calculated on a grid up to 100 mas angular separation from the star. An artificial planet with a photon-based S/N~ 5 is located in the lower right at 67 mas from the center. Left: J′ without positivity constraint on the flux. The image is symmetric, and the contrast is low such that the planet position cannot be inferred. Middle: J″ with a simple positivity constraint on the planet flux. The spatial degeneracy is removed, and the most likely planet position in the lower right indicates the correct planet position. Two side lobes with similar cost values to the true planet position are visible. Right: Cost function J_reg with a positivity constraint on the flux and spectral regularization. The overall contrast is enhanced, and the side lobes are suppressed compared with the un-regularized cost function.