Abstract. 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.

中文翻译：

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基于正则化的基于Curvelet域联合统计模型的光学卫星图像恢复调制传递函数补偿

摘要。调制传递函数 (MTF) 的重尾特性通常会在 MTF 补偿 (MTFC) 努力中引入噪声和混叠效应，以提高光学卫星图像的空间质量。这些退化效应会损害图像的信噪比 (SNR)。因此，用户必须评估图像清晰度与 SNR 对其应用的相对重要性，以决定 MTFC 处理是否合适。我们提出了一种高保真 MTFC 方法，该方法在图像恢复过程中执行噪声正则化和细节保留之间的最佳权衡来解决这个问题。为此，我们利用图像先验特征在混合域中图像的局部平滑度和非局部自相似性方面的优点（即，空间空间和频率）来设计反映这些图像属性的有效正则化项。此外，我们在曲波域中建立了一个简单的联合统计模型来结合这两个属性。为了使这种基于正则化的 MTFC 方法易于处理和健壮，我们采用多目标双层优化方法来解决 MTFC 的严重不适定逆问题。我们进行了大量实验，使用从 IKONOS 的 2A 级产品模拟的合成模糊图像和具有未知模糊的真实卫星图像来评估所提出的基于正则化的 MTFC 方法。图像质量的定量测量表明，所提出的方法以最小的计算复杂度产生有竞争力的恢复结果，并表现出良好的收敛性。