Identifying objects in given data is a task frequently encountered in many applications. Finding vehicles or persons in video data, tracking seismic waves in geophysical exploration data, or predicting a storm front movement from meteorological measurements are only some of the possible applications. In many cases, the object of interest changes its form or position from one measurement to another. For example, vehicles in a video may change its position or angle to the camera in each frame. Seismic waves can change its arrival time, frequency, or intensity depending on the sensor position. Storm fronts can change its form and position over time. This complicates the identification and tracking as the algorithm needs to deal with the changing object over the given measurements. In a previous work, the authors presented a new algorithm to solve this problem - Object reconstruction using K-approximation (ORKA). The algorithm can solve the problem at hand but suffers from two disadvantages. On the one hand, the reconstructed object movement is bound to a grid that depends on the data resolution. On the other hand, the complexity of the algorithm increases exponentially with the resolution. We overcome both disadvantages by introducing an iterative strategy that uses a resampling method to create multiple resolutions of the data. In each iteration the resolution is increased to reconstruct more details of the object of interest. This way, we can even go beyond the original resolution by artificially upsampling the data. We give error bounds and a complexity analysis of the new method. Furthermore, we analyze its performance in several numerical experiments as well as on real data. We also give a brief introduction on the original ORKA algorithm. Knowledge of the previous work is thus not required.

翻译：在给定数据中识别物体是许多应用中常见的问题。例如，在视频数据中寻找车辆或人物、在地球物理勘探数据中追踪地震波、或从气象测量中预测风暴锋面移动，仅是其中一部分应用。在许多情况下，目标物体在不同测量中会改变其形态或位置。例如，视频中的车辆可能在每一帧改变其位置或相对于摄像机的角度；地震波可能因传感器位置不同而改变到达时间、频率或强度；风暴锋面则可能随时间改变形态和位置。这些问题使得识别与追踪变得复杂，因为算法需要处理测量数据中变化的物体。在先前的工作中，作者提出了一种解决该问题的新算法——基于K近似的物体重建（ORKA）。该算法能够处理当前问题，但存在两个缺点：一方面，重建的物体运动受限于依赖数据分辨率的网格；另一方面，算法的复杂度随分辨率呈指数级增长。我们通过引入一种迭代策略克服了这两个缺点，该策略使用重采样方法生成数据的多个分辨率。在每次迭代中，提高分辨率以重建目标物体的更多细节。通过这种方式，我们甚至可以通过人为上采样数据超越原始分辨率。我们给出了新方法的误差界和复杂度分析，并通过多个数值实验和真实数据分析了其性能。此外，我们简要介绍了原始ORKA算法，因此无需了解先前的工作。