Multiband Image Fusion with Controllable Error Guarantees

Abstract

Multiband fusion involves combining an image having high spatial and low spectral resolution with another image having low spatial and high spectral resolution—resulting in a single multiband image with high spatial and spectral resolutions. In classical variational techniques, this problem is formulated as the minimization of an objective function consisting of two quadratic data-fidelity terms and an edge-preserving regularizer; the former account for blur, resolution mismatch and additive noise. In this work, we explore a constrained formulation of this problem where the regularization function is minimized subject to hard constraints on the data fidelity. Unlike the penalty approach, the advantage is that the user has direct control on the data fidelity of the reconstruction. We come up with an efficient ADMM solver for this constrained optimization problem. Moreover, for convex regularizers, we prove that that the ADMM iterates converge to an optimal solution (this is somewhat standard but requires the verification of certain technical conditions). To our knowledge, the use of constrained optimization for image fusion is novel. The proposed framework is shown to model the observations well and its fusion quality is competitive with state-of-the-art methods.