In this paper we introduce a mathematical model of the image saturation phenomenon occurring in a charged coupled device (CCD), and we propose a novel computational method for restoring saturated images acquired by the atmospheric imaging assembly (AIA) telescope. The mathematical model takes into account both primary saturation, when the photon-induced charge reaches the CCD full well capacity, and the blooming effect, when the excess charge flows into adjacent pixels. The restoration of AIA saturated images is then formulated as an inverse problem with a forward operator encoding the standard diffraction of light rays by a convolution, the primary saturation by an upper limit to the number of photons and the blooming effect by the conservation of the photon-induced charge spilled over adjacent pixels. As a result of this theoretical formulation we propose an adaptive ℓ ₁ regularized inversion method improving the desaturation capabilities of the existing SE-DESAT method [Guastavino S etal 2019 Astrophys. J. 882 109]. We prove that this method has the consistency estimation property also in the case that a fixed unknown background is considered. We test the adaptive method both in the case of synthetic and real data, comparing the performance with the one of the SE-DESAT method, showing that the proposed method avoids edge effects and artifacts in reconstructions even when the background solar activity is particularly intense.

在本文中，我们介绍了在电荷耦合器件（CCD）中发生的图像饱和现象的数学模型，并提出了一种新颖的计算方法，用于还原由大气成像组件（AIA）望远镜采集的饱和图像。该数学模型考虑了光子感应电荷达到CCD的全阱容量时的主饱和，以及多余电荷流入相邻像素时的光晕效应。然后将AIA饱和图像的恢复公式化为一个反问题，其中前向算子通过卷积对光线的标准衍射进行编码，初级饱和度通过对光子数量的上限进行编码，光晕效应通过光子守恒来编码引起的电荷溢出到相邻像素上。ℓ ₁正则化反演方法改善现有SE-DESAT方法去饱和的能力[古斯塔维诺小号等人2019 Astrophys。J. 882 109]。我们证明了该方法在考虑固定未知背景的情况下也具有一致性估计性质。我们在合成数据和真实数据的情况下都测试了自适应方法，并将其性能与SE-DESAT方法之一进行了比较，结果表明，即使背景太阳活动特别激烈，该方法也可以避免边缘效应和伪影。