Remote sensing and geophysical imaging techniques are often limited in terms of spatial resolution. This prevents the characterization of physical properties and processes at scales finer than the spatial resolution provided by the imaging sensor. In the last decade, multiple-point statistics simulation has been successfully used for downscaling problems. In this approach, the missing fine-scale structures are imported from a training image which describes the correspondence between coarse and equivalent fine-scale structures. However, in many cases, large variations in the amplitude of the imaged physical attribute, known as trends, pose a challenge for the detection and simulation of these fine-scale features. Here, we develop a novel multiple-point statistics simulation method for downscaling coarse-resolution images with trends. The proposed algorithm relies on a multi-scale sequential simulation framework. Trends in the data are handled by an inbuilt decomposition of the target variable into a deterministic trend component and a stochastic residual component at multiple scales. We also introduce the application of kernel weighting for computing distances between data events and probability aggregation operations for integrating different support data based on a distance-to-probability transformation function. The algorithm is benchmarked against two-point and multiple-point statistics simulation methods, and a deterministic interpolation technique. Results show that the approach is able to cope with non-stationary data sets and scenarios in which the statistics of the training image differ from the conditioning data statistics. Two case studies using digital elevation models of mountain ranges in Switzerland illustrate the method.

中文翻译：

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使用多点统计仿真将具有趋势的图像按比例缩小：在数字高程模型中的应用

遥感和地球物理成像技术通常在空间分辨率方面受到限制。这会阻止以比成像传感器提供的空间分辨率更精细的比例来表征物理特性和过程。在过去的十年中，多点统计仿真已成功用于缩小规模的问题。在这种方法中，从训练图像中导入丢失的精细尺度结构，该训练图像描述了粗略和等效的精细尺度结构之间的对应关系。但是，在许多情况下，成像物理属性的幅度的大变化（称为趋势）对这些精细尺度特征的检测和仿真提出了挑战。在这里，我们开发了一种新颖的多点统计模拟方法，用于按比例缩小具有趋势的粗分辨率图像。所提出的算法依赖于多尺度顺序仿真框架。数据趋势通过将目标变量内置分解为确定性趋势分量和随机残差分量进行多尺度处理。我们还介绍了核加权在计算数据事件之间的距离以及基于概率到概率转换函数集成不同支持数据的概率聚合操作中的应用。该算法针对两点和多点统计仿真方法以及确定性插值技术进行了基准测试。结果表明，该方法能够应对训练图像统计量与条件数据统计量不同的非平稳数据集和场景。