Airborne gravimetry data sparse reconstruction via L1-norm convex quadratic programming

基于L1范数凸二次规划方法的航空重力测量数据稀疏重构（英文）

In practice, airborne gravimetry is a sub-Nyquist sampling method because of the restrictions imposed by national boundaries, financial cost, and database size. In this study, we analyze the sparsity of airborne gravimetry data by using the discrete Fourier transform and propose a reconstruction method based on the theory of compressed sensing for large- scale gravity anomaly data. Consequently, the reconstruction of the gravity anomaly data is transformed to a Ll-norm convex quadratic programming problem. We combine the preconditioned conjugate gradient algorithm （PCG） and the improved interior-point method （IPM） to solve the convex quadratic programming problem. Furthermore, a flight test was carried out with the homegrown strapdown airborne gravimeter SGA-WZ. Subsequently, we reconstructed the gravity anomaly data of the flight test, and then, we compared the proposed method with the linear interpolation method, which is commonly used in airborne gravimetry. The test results show that the PCG-IPM algorithm can be used to reconstruct large-scale gravity anomaly data with higher accuracy and more effectiveness than the linear interpolation method.

由于受到国界、测量成本和数据规模等因素的限制,航空重力测量本质上是一种欠奈奎斯特采样方法,本文通过离散傅里叶变换分析了航空重力测量的稀疏性,提出了利用压缩感知理论实现大规模重力异常数据高精度重构的思路。基于压缩感知理论,重力异常数据重构问题可以转化为基于L1范数的凸二次规划问题,本文结合预处理共轭梯度算法,提出了一种改进的内点法来解决此问题。进一步地,我们利用自主研发的SGA-WZ型捷联式航空重力仪在中国某地区进行了航空重力测量试验。通过对试验中测得的重力异常数据进行重构,与常用的线性插值重构方法对比,结果表明:本文提出的基于压缩感知理论的新方法能够以更高的重构精度,更有效地解决大规模重力异常数据的重构问题。