基于小波的尺度稳健性评估及其应用
Robust Wavelet-based Assessment of Scaling with Applications
摘要：
许多方法已经处理了自相似性的统计评估，其中许多是基于多尺度概念。大多数依赖于某些分布假设，而这些假设通常被实际数据迹线所违背，其特征往往是大的时间或空间平均水平偏移、缺失值或极端观测。提出了一种基于Theil型加权回归的二维数据（图像）自相似性估计方法。该方法相比，两个传统的估计技术，使用小波分解，普通最小二乘（OLS）和Abry-维奇偏差校正估计（AV）。作为一个应用，从鲁棒方法产生的自相似性估计的适用性被示出为在数字化乳房X线照片图像分类为癌性或非癌性中的预测特征。这里采用的诊断是基于图像背景的属性，这通常是乳腺癌筛查中未使用的模式。分类结果表明，近68%的准确率，略有不同的小波基的选择，和使用的多分辨率水平的范围。
英文摘要：
A number of approaches have dealt with statistical assessment of self-similarity, and many of those are based on multiscale concepts. Most rely on certain distributional assumptions which are usually violated by real data traces, often characterized by large temporal or spatial mean level shifts, missing values or extreme observations. A novel, robust approach based on Theil-type weighted regression is proposed for estimating self-similarity in two-dimensional data (images). The method is compared to two traditional estimation techniques that use wavelet decompositions; ordinary least squares (OLS) and Abry-Veitch bias correcting estimator (AV). As an application, the suitability of the self-similarity estimate resulting from the the robust approach is illustrated as a predictive feature in the classification of digitized mammogram images as cancerous or non-cancerous. The diagnostic employed here is based on the properties of image backgrounds, which is typically an unused modality in breast cancer screening. Classification results show nearly 68% accuracy, varying slightly with the choice of wavelet basis, and the range of multiresolution levels used.
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