基于稀疏重建的航空货运量模型研究

Sparse Recovery Model of Air Cargo Volume

压缩感知(Compressed Sensing CS)理论广泛应用于应用数学、图像重建、信道估计以及谱估计等不同领域.在理论方面,依据压缩感知基本理论建立差分稀疏凸优化模型,并推导差分稀疏重建限制子空间特征值的稳定性条件;在应用方面,研究此模型在我国航空货运量建模与预测中的应用,以1998-2007年我国航空货运量的统计数据为基础,利用凸优化理论建立我国航空货运量的差分稀疏模型.通过拟合误差指标的详细比较可知:相对于灰色理论模型、回归分析模型,航空货运量的差分稀疏模型具有更高拟合精度.实验证明,差分稀疏理论可以为航空货运量的短期预测以及航空货运业调控提供有效理论支持.

Theory of Compressed Sensing can be found in many different fields, such as image processing, channel estimation, spectrum estimation, In this paper, we mainly study difference sparse convex optimization, and provide the stability of difference sparse convex optimization in the view of 1.-Constrained Minimal Singular Value（/.-CMSV）; we also apply this method in the field of air cargo volume based on mainly idea of CS. Basing on air cargo volume statistical data in China from the year 1998 to 2007, the spm-se recovery model of air cargo volume is established by the CVX tool of matlab. The test results show that sparse recovery model is more suitable than GM（1,1） model and regression analysis model, and difference sparse model of air cargo volume can provide some effective theory evidence to forecast short-term aeronautic cargo capacity and supervise the native aeronautic cargo market.