NMR data processing using iterative thresholding and minimum l₁-norm reconstruction

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• 作者：Alan S. Stern ; David L. Donoho ; Jeffrey C. Hoch
• 关键词：Spectrum analysis ; Non-Fourier methods ; Signal processing ; Maximum entropy
• 刊名：Journal of Magnetic Resonance
• 出版年：2007
• 出版时间：October 2007
• 年：2007
• 卷：188
• 期：2
• 页码：295-300
• 全文大小：226 K

文摘

Iterative thresholding algorithms have a long history of application to signal processing. Although they are intuitive and easy to implement, their development was heuristic and mainly ad hoc. Using a special form of the thresholding operation, called soft thresholding, we show that the fixed point of iterative thresholding is equivalent to minimum l₁-norm reconstruction. We illustrate the method for spectrum analysis of a time series. This result helps to explain the success of these methods and illuminates connections with maximum entropy and minimum area methods, while also showing that there are more efficient routes to the same result. The power of the l₁-norm and related functionals as regularizers of solutions to underdetermined systems will likely find numerous useful applications in NMR.