fg-ORKA: fast and gridless reconstruction of moving and deforming objects in multidimensional data

Identifying and tracking objects over multiple observations is a frequent task in many applications. Traffic monitoring requires the tracking of vehicles or pedestrians in video data and geophysical exploration relies on identifying seismic wave fronts from data of multiple sensors, only to mention two examples. In many cases, the object changes its shape or position within the given data from one observation to another. Vehicles can change their position and angle relative to the camera while seismic waves have different arrival times, frequencies, or intensities depending on the sensor position. This complicates the task at hand. In a previous work, the authors presented a new algorithm to solve this problem—object reconstruction using K-approximation (ORKA). This algorithm is hindered by two conflicting limitations: the tracked movement is limited by the sampling grid while the complexity increases exponentially with the resolution. We introduce an iterative variant of the ORKA algorithm that is able to overcome this conflict. We also give a brief introduction on the original ORKA algorithm. Knowledge of the previous work is thus not required. We give theoretical error bounds and a complexity analysis which we validate with several numerical experiments. Moreover, we discuss the influence of different parameter choices in detail. The results clearly show that the iterative approach can outperform ORKA in both accuracy and efficiency. On the example of video processing we show that the new method can be applied where the original algorithm is too time and memory intensive. Furthermore, we demonstrate on seismic exploration data that we are now able to recover much finer details on the wave front movement then before.