Tomographic inversion using ℓ1-norm regularization of wavelet coefficients

We propose the use of ℓ₁ regularization in a wavelet basis for the solution of linearized seismic tomography problems   A m = d   , allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution m that contains no more fine-scale structure than is necessary to fit the data d to within its assigned errors.     

自适应阈值方法去除风廓线雷达地物杂波

风廓线雷达探测过程中电磁波传输会受到各类杂波的干扰,其中,地物是主要来源。从功率谱数据上看,地物杂波主要集中在零频附近,且幅度较高,不加以抑制会影响气象回波的识别。针对目前常用的小波阈值滤波法在处理近零频回波被杂波覆盖时效果不佳的情况,该文结合风廓线雷达特点,提出一种根据小波分解高频系数自适应确定阈值的方法,并通过模拟数据与风廓线雷达实测数据进行检验,结果表明:即便信号靠近零频,且被杂波覆盖,该方法也能快速准确识别信号回波。同时,该算法原理简单、计算量小、易于实现,在实际应用中能够增加谱峰识别准确率,可为改善风廓线雷达产品质量提供参考。     

Gaussian反对称小波与SAR影像目标特征提取

由于遥感影像中目标尺度的不确定性 ,使得在目标特征提取和检测前难以事先确定最佳尺度以适应影像空间不同尺度目标的识别与检测 ,给遥感影像自动识别与全自动数字摄影测量带来了极大困难。为了解决遥感影像中不同尺度目标的探测问题 ,提出基于一般高斯核构造一类Gaussian反对称小波并给出相应二维小波变换的快速算法 ,弥补了MallatGaussian小波 (σ =1)在解决遥感影像空间不同尺度目标检测中的不足。对于影像中不同尺度的目标特征探测 ,通过在Gaussian核函数中选择适当的参数σ值 ,得到相应的反对称小波空间滤波器响应系数 ,用于解决不同目标的检测问题。分别给出了有关Gaussian反对称小波的 5组空间滤波器响应系数 ,对于研究遥感影像目标兴趣算子和多源遥感影像特征检测尤为重要。由于SAR影像中“speckles”是一乘性噪声 ,文中先对原SAR影像进行对数变换得到一同态影像。基于小波变换的软域值斑点噪声抑制既在一定程度上抑制斑点噪声又保持影像细节信息。通过对两SAR影像检测实验 ,表明给出的Gaussian反对称小波类在遥感影像特征检测中效果极佳。遥感影像中同时存在阶跃型和屋脊型边缘 ,可以采用反对称小波的极大模或过零点检测提取影像边缘特征 ,但得到的结果存在局部位置偏差。这一结论对于今后研究     

The Use of Second-generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-levelling Data

The merging of a gravimetric quasigeoid model with GPS-levelling data using second-generation wavelets is considered so as to provide better transformation of GPS ellipsoidal heights to normal heights. Since GPS-levelling data are irregular in the space domain and the classical wavelet transform relies on Fourier theory, which is unable to deal with irregular data sets without prior gridding, the classical wavelet transform is not directly applicable to this problem. Instead, second-generation wavelets and their associated lifting scheme, which do not require regularly spaced data, are used to combine gravimetric quasigeoid models and GPS-levelling data over Norway and Australia, and the results are cross-validated. Cross-validation means that GPS-levelling points not used in the merging are used to assess the results, where one point is omitted from the merging and used to test the merged surface, which is repeated for all points in the dataset. The wavelet-based results are also compared to those from least squares collocation (LSC) merging. This comparison shows that the second-generation wavelet method can be used instead of LSC with similar results, but the assumption of stationarity for LSC is not required in the wavelet method. Specifically, it is not necessary to (somewhat arbitrarily) remove trends from the data before applying the wavelet method, as is the case for LSC. It is also shown that the wavelet method is better at decreasing the maximum and minimum differences between the merged geoid and the cross-validating GPS-levelling data.     

Statistical Classification of Different Petrographic Varieties of Aggregates by Means of Near and Mid Infrared Spectra

The increasing interest of the construction aggregates industry in reducing production costs and the costs resulting from improper use of construction materials leads to the question whether it is possible to statistically identify some rock variants by their reflectivity of near-infrared and mid-infrared light. Infrared spectroscopy allows quantitative and qualitative analysis of minerals in a reliable manner, whereas the classification of rocks is complicated by the fact that the optic behavior of minerals forming the rock often appears muted. In addition, minor constituents may dominate the spectrum. Furthermore the relevant spectra form high dimensional data, which are extremely difficult to analyse statistically, especially when curves are very similar. Common methods of multivariate statistics for this type of data, used in chemometric studies, followed by linear discriminant analysis, do not lead to acceptable classification error rates. In this paper wavelets are used in order to reduce dimensionality. As wavelets are better able to mirror local behavior of curves, they are more suitable for selecting characteristic features. The approximation is analyzed in terms of its classification properties using Mahalanobis distance or flexible discriminant analysis.     

Wavelet-based correlation (WBC) of zoned crystal populations and magma mixing

Magma mixing is a common process and yet the rates, kinematics and numbers of events are difficult to establish. One expression of mixing is the major, trace element, and isotopic zoning in crystals, which provides a sequential but non-monotonic record of the creation and dissipation of volumes of distinct chemical potential. We demonstrate a wavelet-based correlation (WBC) technique that uses this zoning for the recognition of the minimum number of mixing, or open-system events, and the criteria for identifying populations of crystals that have previously shared a mixing event. When combined with field observations of the spatial distribution of crystal populations, WBC provides a statistical link between the time-varying thermodynamic and fluid dynamic history of the magmatic system. WBC can also be used as a data mining utility to reveal open-system events where outcrop is sparse. An analysis of zoned plagioclase from the Tuolumne Intrusive Suite provides a proof of principle for WBC.     

中国"代"尺度气候预测

将子波分析技术与随机动力学相结合,提出了突变点数建模代尺度气候预测新技术—突变点数建模技术,并将该技术应用于中国不同地区代尺度的干湿驰豫时间的预报。研究结果表明,在代尺度上,我国北方、西南和东南气候灾害频繁,南方多涝,西北和北方(不包括东北)则多旱。由于该技术是关于时间序列建模的,故可以应用到水文、地震、生态等领域有关的建模和预测。