M-Smoother with local Linear Fit

Abstract

Local linear M-smoothing is proposed as a method for noise reduction in one-dimensional signals. It is more appropriate than conventional local linear smoothing, because it does not introduce blurring of jumps in the signal. It improves local constant M-smoothing, by avoiding boundary effects at edges and jumps. While the idea of local linear M-smoothing is straightforward, numerical issues are challenging, because of the local minima aspect that is crucial to good performance. We give an algorithm which is both fast and robust together with the theoretical properties of the local linear M-smoother. The new M-smoother gives a large improvement for some data sets compared to the local constant M-smoother and demonstrates elsewhere good performance on various artificial and magnetic resonance data sets.

Keywords:

• Local Linear Fit
• M-estimation
• Nonparametric Regression
• Jump Preservation
• Noise Reduction