Robust smoothing of gridded data in one and higher dimensions with missing values

Area of Science:

• Data Science
• Applied Mathematics
• Signal Processing

Background:

• Data smoothing is crucial for noise reduction and pattern identification in uniformly-sampled datasets.
• Existing methods may lack automation, robustness to outliers, or efficiency in higher dimensions.

Purpose of the Study:

• To present a fully automated, fast, and robust smoothing procedure for uniformly-sampled data.
• To enable automatic selection of smoothing parameters.
• To provide a tool applicable to one and higher dimensional data.

Main Methods:

• The algorithm employs a penalized least squares method.
• The discrete cosine transform (DCT) is utilized for efficient computation.
• Generalized cross-validation (GCV) is used for automatic smoothing parameter selection.
• An iteratively reweighted least squares approach ensures robustness against missing and outlying values.

Main Results:

• The proposed method achieves fast and automatic smoothing in one to higher dimensions.
• Robustness to missing and outlying data is demonstrated.
• The algorithm requires low storage, enhancing its practicality.
• Simplified and user-friendly Matlab codes are provided for implementation.

Conclusions:

• The developed algorithm offers an efficient, automatic, and robust smoothing solution.
• It is suitable for a wide range of data analysis applications.
• The provision of Matlab code facilitates its adoption and use.