Deconvolution When Classifying Noisy Data Involving Transformations

• 成果类型: Article
• 署名作者: Carroll, Raymond; Delaigle, Aurore; Hall, Peter
• 署名单位: Texas A&M University System; Texas A&M University College Station; University of Melbourne
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.699793
• 发表日期: 2012
• 页码: 1166-1177
• 关键词: blind deconvolution; DISCRIMINANT-ANALYSIS; statistical-analysis; edge-detection; image; restoration; CLASSIFICATION; RECOVERY; signal

摘要

In the present study, we consider the problem of classifying spatial data distorted by a linear transformation or convolution and contaminated by additive random noise. In this setting, we show that classifier performance can be improved if we carefully invert the data before the classifier is applied. However, the inverse transformation is not constructed so as to recover the original signal, and in fact, we show that taking the latter approach is generally inadvisable. We introduce a fully data-driven procedure based on cross-validation, and use several classifiers to illustrate numerical properties of our approach. Theoretical arguments are given in support of our claims. Our procedure is applied to data generated by light detection and ranging (Lidar) technology, where we improve on earlier approaches to classifying aerosols. This article has supplementary materials online.