Regularization-based modulation transfer function compensation for optical satellite image restoration using joint statistical model in curvelet domain

The heavy-tailed properties of modulation transfer function (MTF) typically introduce noise and an aliasing effect in the MTF compensation (MTFC) effort to improve the spatial quality of optical satellite images. These degradative effects compromise the image’s signal-to-noise ratio (SNR). Consequently, users must evaluate the relative importance of image sharpness versus SNR for their applications to decide whether MTFC processing is appropriate. We propose a high-fidelity MTFC method that executes an optimal trade-off between noise regularization and detail preservation in the image restoration process to address this problem. To this end, we exploit the merit of image prior characteristics in both local smoothness and nonlocal self-similarity properties of an image in a hybrid domain (viz., space spatial and frequency) to design effective regularization terms that reflect these image properties. Furthermore, we establish a simple joint statistical model in the curvelet domain to combine these two properties. To make this regularization-based MTFC method tractable and robust, we employ the multiobjective bilevel optimization approach to solve the severely ill-posed inverse problem of MTFC. We conduct extensive experiments to evaluate the proposed regularization-based MTFC method using synthetically blurred images simulated from the level 2A product of IKONOS and real satellite images with unknown blur. Quantitative measurements of image quality reveal that the proposed method produces competitive restoration results with minimum computational complexity and exhibits a good convergence property. These experimental results show that the proposed method can find a compromise between regularizing noise and preserving image fidelity.