基于DCT的广义指数阈值衰减凸集投影算法在位场数据补空中的应用

Interpolation of potential-field data by Projection Onto Convex Sets algorithm with generalized exponential threshold and based on Discrete Cosine Transform

数据补空或插值是位场数据处理中一个非常基本且重要的问题,在野外数据测量过程中遇到水域、断崖等情况时无法进行数据采集,导致数据出现缺失情况。为了便于后续数据处理,需要对缺失数据体进行补全。本文将离散余弦变换(DCT)应用到凸集投影(POCS)算法中来补全位场缺失数据,并给出了广义指数阈值衰减方式。模型试验及实例应用表明,基于DCT并结合广义指数阈值衰减形式的POCS算法具有数据补空精度高、补空痕迹小和补空数据噪声含量更接近真实情况等优点。

Data filling or interpolation is a fundamental and vital problem of potential-field data processing.Some data cannot be measured when some places are unable to reach,such as rivers,or cliffs.If we want to acquire the missing data for better subsequent processing,we need to interpolate or fill in the missing data.Hence,this article introduces the Discrete Cosine Transform(DCT) method into the Projection Onto Convex Sets(POCS) algorithm to tackle this problem,and a generalized exponential threshold attenuation method is also given.Finally,model tests and practical applications show that the POCS algorithm with generalized exponential threshold and based on DCT has the advantages of high accuracy,small filling or interpolating traces and the noise standard of the filled data are closer to real situation.