This dissertation presents a general framework for changepoint detection based on L0 model selection. The core method, Iteratively Reweighted Fused Lasso (IRFL), improves upon the generalized lasso by adaptively reweighting penalties to enhance support recovery and minimize criteria such as the Bayesian Information Criterion (BIC). The approach allows for flexible modeling of seasonal patterns, linear and quadratic trends, and autoregressive dependence in the presence of changepoints. Simulation studies demonstrate that IRFL achieves accurate changepoint detection across a wide range of challenging scenarios, including those involving nuisance factors such as trends, seasonal patterns, and serially correlated errors. The framework is further extended to image data, where it enables edge-preserving denoising and segmentation, with applications spanning medical imaging and high-throughput plant phenotyping. Applications to real-world data demonstrate IRFL's utility. In particular, analysis of the Mauna Loa CO2 time series reveals changepoints that align with volcanic eruptions and ENSO events, yielding a more accurate trend decomposition than ordinary least squares. Overall, IRFL provides a robust, extensible tool for detecting structural change in complex data.

翻译：本论文提出了一种基于L0模型选择的变点检测通用框架。核心方法——迭代重加权融合Lasso（IRFL）——通过自适应重加权惩罚项改进了广义lasso，以增强支撑集恢复能力并最小化贝叶斯信息准则（BIC）等指标。该方法允许在存在变点的情况下灵活建模季节性模式、线性和二次趋势以及自回归依赖性。仿真研究表明，IRFL在包括趋势、季节性模式和序列相关误差等干扰因素的广泛挑战性场景中均能实现精确的变点检测。该框架进一步扩展到图像数据领域，可实现边缘保持去噪与分割，其应用范围涵盖医学影像和高通量植物表型分析。实际数据应用验证了IRFL的实用性。特别是对莫纳罗亚火山CO2时间序列的分析显示，检测到的变点与火山爆发和ENSO事件高度吻合，相比普通最小二乘法能获得更精确的趋势分解结果。总体而言，IRFL为检测复杂数据结构变化提供了一个鲁棒且可扩展的工具。