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：本文提出了一种基于L0模型选择的变点检测通用框架。其核心方法——迭代重加权融合套索（IRFL）——通过自适应地重新加权惩罚项，改进了广义套索，增强了支持恢复能力，并最小化了诸如贝叶斯信息准则（BIC）等准则。该方法允许在存在变点的情况下灵活地对季节性模式、线性及二次趋势以及自回归依赖性进行建模。模拟研究表明，IRFL在多种具有挑战性的场景中实现了准确的变点检测，包括那些涉及趋势、季节性模式及序列相关误差等干扰因素的场景。该框架进一步扩展至图像数据，实现了边缘保持去噪与分割，应用领域涵盖医学成像和高通量植物表型分析。对真实世界数据的应用证明了IRFL的实用性。特别是对冒纳罗亚二氧化碳时间序列的分析揭示了与火山喷发和ENSO事件一致的变点，相较于普通最小二乘，得到了更准确的趋势分解。总体而言，IRFL为检测复杂数据中的结构变化提供了一个鲁棒且可扩展的工具。