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.
翻译:一些方法涉及对自异性的统计评估,其中许多方法以多尺度概念为基础,多数依赖某些通常被真实数据痕迹所违反的分布假设,其特征往往是巨大的时间或空间平均水平变化、缺失值或极端观察。提出了基于Theil型加权回归的新颖、稳健的方法,以估算二维数据(图像)中的自异性。这种方法与两种传统估算技术进行比较,这两种技术使用波盘分解法;普通最小平方和Abry-Vitch偏差校准估计值(AV)。作为一种应用,强健方法产生的自异性估计值的适宜性被描述为将数字化乳房X线图象分类为癌症或非癌症的预测特征。这里采用的诊断基于图像背景的特性,通常是乳腺癌筛查中的一种未使用的方法。分类结果显示近68%的准确性,与波盘选择基础和使用的多分辨率范围略有不同。