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Extensions to minimum relative entropy inversion for noisy data.

Tadeusz J Ulrych1, Allan D Woodbury

  • 1Earth and Ocean Sciences, University of British Columbia, Vancouver, British Columbia, Canada. ulrych@eos.ubc.ca

Journal of Contaminant Hydrology
|November 11, 2003
PubMed
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Minimum relative entropy (MRE) effectively reconstructs plume sources from noisy data, outperforming Tikhonov regularization (TR). Estimating MRE

Area of Science:

  • Environmental Science
  • Geosciences
  • Applied Mathematics

Background:

  • Previous studies compared Minimum Relative Entropy (MRE) and Tikhonov Regularization (TR) for plume source reconstruction.
  • Neupauer et al. (2000) previously compared MRE and TR on a specific groundwater contamination problem.
  • The performance of TR can be suboptimal for inverse problems involving delta-like sources and noisy, diffuse data.

Purpose of the Study:

  • To re-evaluate and demonstrate the effectiveness of MRE compared to TR for inverse problems, particularly with noisy data.
  • To show that MRE provides superior resolution for reconstructing delta-like sources from diffuse groundwater contamination data.
  • To illustrate methods for estimating the hyperparameter (epsilon) required for MRE solutions in noisy conditions.

Main Methods:

Related Experiment Videos

  • Comparison of MRE and TR on a plume source reconstruction problem.
  • Convolution of delta-like sources with diffuse groundwater contamination response functions.
  • Application of MRE with hyperparameter estimation using data residuals, real cepstrum, and Akaike Information Criterion (AIC).

Main Results:

  • Tikhonov regularization (TR) demonstrated poor performance on problems with delta-like sources convolved with diffuse response functions, especially under noisy conditions.
  • Minimum relative entropy (MRE) successfully resolved multiple delta-like spikes from noisy, diffuse data, indicating excellent performance.
  • Estimation of the MRE hyperparameter (epsilon) was shown to be feasible using various data-driven approaches.

Conclusions:

  • Minimum relative entropy (MRE) is a robust and effective method for solving noisy inverse problems in groundwater contamination studies.
  • MRE offers superior resolution for plume source reconstruction compared to Tikhonov regularization (TR) when dealing with delta-like sources and diffuse data.
  • The study confirms the practical utility and reliability of MRE for environmental inverse problems.