说明：  介绍了一种图像重建的变分模型，并对其进行了功能分析。空间。模型的特点是通过相对于Riesz基进行基变换，然后进行区间约束来实现数据精确性。该设置特别涉及重构受限于从JPEG或JPEG 2000压缩les获得的数据的图像的任务。作为图像先验，采用任意阶的广义广义变分（TGV）函数。本文是该模型解析和数值两方面工作的第一篇，对函数空间进行了全面的分析，为具体应用提供了具体实例。在一般情形下，得到了一个新的非强制性存在性结果和最优性条件，包括TGV泛函的次优性的刻画。
(A variational model for image reconstruction is introduced and analyzed in function space. Specic about the model is the data delity which is realized via a basis transforma-tion with respect to a Riesz basis followed by interval constraints. This setting in particular covers the task of reconstructing images constrained to data obtained from JPEG or JPEG 2000 compressed les. As image prior, the Total Generalized Variation (TGV) functional of arbitrary order is employed. The present paper, being the rst of two works that deal with both analytical and numerical aspects of the model, provides a comprehensive anal-ysis in function space and denes concrete instances for particular applications. A new,non-coercive existence result and optimality conditions, including a characterization of the subdierential of the TGV functional, are obtained in the general setting.)