Entropy metric regularization for computational imaging with sensor arrays

Correlative interferometric image reconstruction is a computational imaging approach for synthesizing images from sensor arrays and relies on estimating source intensity from the cross-correlation across near-field or far-field measurements from multiple sensors of the arrays. Key to using the approach is the exploitation of relationship between the correlation and the source intensity. This relationship is of a Fourier transform type when the sensors are in the far-field of the source and the velocity of wave propagation in the intervening medium is constant. Often the estimation problem is ill-posed resulting in unrealistic reconstructions of images. Positivity constraints, boundary restrictions, ℓ1 regularization, and sparsity constrained optimization have been applied in previous work. This paper considers the noisy case and formulates the estimation problem as least squares minimization with entropy metrics, either minimum or maximum, as regularization terms. Situations involving far-field interferometric imaging of extended sources are considered and results illustrating the advantages of these entropy metrics and their applicability are provided.