数学
正交基
二次方程
反问题
规范(哲学)
应用数学
阈值
迭代法
约束(计算机辅助设计)
基础(线性代数)
算法
反向
理想(伦理)
非线性系统
数学优化
计算机科学
数学分析
图像(数学)
人工智能
哲学
几何学
物理
法学
认识论
量子力学
政治学
作者
Ingrid Daubechies,Michel Defrise,Christine De Mol
摘要
Abstract We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary preassigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted 𝓁 p ‐penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem. Use of such 𝓁 p ‐penalized problems with p < 2 is often advocated when one expects the underlying ideal noiseless solution to have a sparse expansion with respect to the basis under consideration. To compute the corresponding regularized solutions, we analyze an iterative algorithm that amounts to a Landweber iteration with thresholding (or nonlinear shrinkage) applied at each iteration step. We prove that this algorithm converges in norm. © 2004 Wiley Periodicals, Inc.
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