Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates

In log-polar coordinates, the conventional data sampling method is to sample uniformly in the log-polar radius and polar angle directions, which makes the sample at the fovea of the data denser than that of the peripheral. The central oversampling phenomenon of the conventional sampling method gives no more efficient information and results in computational waste. Fortunately, the adaptive sampling method is a powerful tool to solve this problem in practice, so the paper introduces it to quantum data processing. In the paper, the quantum representation model of adaptive sampled data is proposed first, in which the upper limit of the sampling number of the polar angles is related to the log-polar radius. Owing to this characteristic, its preparation process has become relatively complicated. Then, in order to demonstrate the practicality of the model given in the paper, the scaling up algorithm with an integer scaling ratio based on biarcuate interpolation and its circuit implementation of quantum adaptive sampled data is given. However, due to the special properties of the adaptive sampling method in log-polar coordinates, the interpolation process of adaptive sampled data becomes quite complicated as well. At the end of this paper, the feasibility of the algorithm is verified by a numerical example.