医学图像三维重建的插值方法研究

本文从算法的形成过程、基本原理和步骤、适用范围和局限性、以及可能的改进方法等对现有三维重建的插值方法作了评述。探讨了各种插值方法之间的内在联系，分析了存在局限性的本质原因。对插值问题的进一步研究方向提出了看法。     

基于城市引力场模型的城镇土地基准地价平衡探讨

城镇基准地价平衡用于协调区域地价,使基准地价能客观地反映出不同城镇之间真实的经济差异和地价水平。本文提出一种基于城市引力场模型的城镇土地基准地价平衡方法,通过考虑中心城镇地价扩散的影响,弥补传统分段线性插值的平衡方法的不足,并以湖北省为例进行实例研究。把平衡结果和通过样点数据测算的基准地价进行对比分析以发现此方法的特点,并对城镇基准地价空间分布的内在规律性进行了初步探讨。     

Suspended sediment transport in a highly erodible catchment: The River Isábena (Southern Pyrenees)

Understanding and quantifying sediment load is important in catchments draining highly erodible materials that eventually contribute to siltation of downstream reservoirs. Within this context, the suspended sediment transport and its temporal dynamics have been studied in the River Isábena (445 km², south-central Pyrenees, Ebro basin) by means of direct sampling and turbidity recording during a 3-year dry period. The average flood-suspended sediment concentration was 8 g l^− 1, with maximum instantaneous values above 350 g l^− 1. The high scatter between discharge and suspended sediment concentrations (up to five orders of magnitude) has not permitted the use of rating curve methods to estimate the total load. Interpolation techniques yielded a mean annual sediment load of 184,253 t y^− 1 for the study period, with a specific yield of 414 t km^− 2 y^− 1. This value resembles those reported for small torrents in nearby mountainous environments and is the result of the high connectivity between the badland source areas and stream courses, a fact that maximises sediment conveyance through the catchment. Floods dominated the sediment transport and yield. However, sediment transport was more constant through time than that observed in Mediterranean counterparts; this can be attributed to the role of base flows that entrain fine sediment temporarily stored in the channel and force the river to carry high sediment concentrations (i.e., generally in the order of 0.5 g l^− 1), even under minimum flow conditions.     

秦岭主脊区年降水量空间插值最优方法研究

利用ARCGIS软件,以研究区多年平均年降水量为数据源,开展以下研究：（1）采用反距离权重法、普通（泛）克里金法、样条函数法和趋势面法进行直接内插。（2）利用降水量随海拔递增率,再次利用以上方法进行插值。（3）分析站点数量的变化对插值精度的影响。（4）分析插值空间尺度变化对插值精度的影响。针对插值结果,使用交叉验证法来评估插值方法的优劣,旨在找出研究区年降水量空间插值的最优方法。结果表明：（1）研究区多年降水量与纬度呈现出很好的负相关,与其他各地理环境因子相关性很差或无相关性。（2）考虑降水随海拔的递增率后,研究区南坡西段和研究区海拔<600 m和>800 m的大部分观测站的空间内插精度得到有效提高,其它区域以及其它海拔区间的插值精度反而降低,因此使用单一线性数据作为整个研究区降水随海拔的变化率不够科学和严谨。（3）在缺少研究区不同剖面降水观测资料的情况下,权重为0.001 的正规则样条函数法是最优插值方法。（4）像元尺度在50～1 000 m间的变化对降水插值的不确定影响甚微;插值精度与选取的插值点个数无明显相关性,当站点个数为20个时,插值精度最高。     

河北地区气温内插模型及检验方

以1965—1999年河北省逐月平均气温为研究对象,采用一元线性回归法和IDW(Inverse Distance Weighted)相结合的方法,将温度插值到河北省整个区域,绘制河北省温度空间分布图,实现河北省年内各月平均气温空间填图;同时,分析了河北省冬季和夏季各月的月平均温度的误差精度。结果表明：插值的结果与观测值的相关系数(R)在12个月均大于0.82,显示插值方法具有较好的模拟精度,可用于气温的空间插值和特征分析。     

空间域位置相关法道间插值

为了消除地震资料空间采样不够造成的空间假频现象,在ｃｌａｅｒｂｏｕｔ空间２－Ｄ预测误差滤波器的启示下,本文提出了空间域位置相关法道内插值,在地面实际资料处理中都取得了良好的效果。     

用一种插值方法作短期气候预测的试验

将ｓｈｅｐａｒｄ插值方法运用到短期气候预测中,建立一类非模式预报方法,按照相似原因将产生相似结果的原理来作预报,对云南降水进行了预报试验。结果表明,这种方法与多元回归相比具有良好的预报能力,值得进一步探讨和应用。     

共炮检距高斯波束偏移的一种快速实现算法

与共炮高斯波束偏移相比,共炮检距高斯波束偏移具有直接抽取炮检距域共成像点道集的优势.过去,共炮检距高斯波束偏移以损失成像精度的代价采用最速下降法来降低积分的维数,从而提高计算效率.但经过最速下降近似简化的偏移公式仍是频率域的,需要在每个频点进行计算.为此,本文提出一种快速实现算法来避免采用最速下降法.本文通过分析一个水平层状速度模型的偏移过程和Marmousi速度模型的成像结果来检验不同插值方法对快速实现算法的成像精度和计算效率的影响,并建议采用二维三次卷积插值方法.同时本文在Marmousi速度模型下验证了快速实现算法相对于最速下降法在成像精度和计算效率上的优势.此外,本文将采用二维三次卷积插值的快速实现算法应用于Sigsbee2A模型并获得了清晰的盐下图像.     

Seismic data interpolation using generalised velocity‐dependent seislet transform

Data interpolation is an important step for seismic data analysis because many processing tasks, such as multiple attenuation and migration, are based on regularly sampled seismic data. Failed interpolations may introduce artifacts and eventually lead to inaccurate final processing results. In this paper, we generalised seismic data interpolation as a basis pursuit problem and proposed an iteration framework for recovering missing data. The method is based on non‐linear iteration and sparse transform. A modified Bregman iteration is used for solving the constrained minimisation problem based on compressed sensing. The new iterative strategy guarantees fast convergence by using a fixed threshold value. We also propose a generalised velocity‐dependent formulation of the seislet transform as an effective sparse transform, in which the non‐hyperbolic normal moveout equation serves as a bridge between local slope patterns and moveout parametres in the common‐midpoint domain. It can also be reduced to the traditional velocity‐dependent seislet if special heterogeneity parametre is selected. The generalised velocity‐dependent seislet transform predicts prestack reflection data in offset coordinates, which provides a high compression of reflection events. The method was applied to synthetic and field data examples, and the results show that the generalised velocity‐dependent seislet transform can reconstruct missing data with the help of the modified Bregman iteration even for non‐hyperbolic reflections under complex conditions, such as vertical transverse isotropic (VTI) media or aliasing.     

自适应多尺度第二代小波配点法探地雷达数值模拟

基于第二代小波变换的提升方案构造了插值小波,将雷达波场函数进行了二维小波变换,得到所有尺度上与计算网格相联系的小波系数和尺度系数.对所有尺度上的小波系数进行分析,根据解的局部性与小波系数阈值的控制,实现网格压缩和配点的自适应调节.保留大于给定阈值的小波系数及对应网格点,令小于给定阈值的小波系数为零,并舍弃其对应网格点.达到光滑区域采用较少的计算网格点,在奇异性较大的区域采用较多的计算网格点的目的.通过对自适应网格进行邻域校正、重构检查等附加修正,推导了场值更新的显式时间迭代方案.最后,以均匀、阶梯与复杂三个典型GPR模型为例,与常规数值计算结果对比表明：自适应小波配点法（AWCM）利用第二代小波的多尺度分解和快速变换的特点,可以使计算网格随着时间步适应解的移动和变化,允许计算资源更有效地使用,具有高压缩率,达到跟踪奇异性的目的,特别适合于探地雷达正演中波传问题的模拟.