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Keywords:

  • Heteroscedastic noise;
  • Linear inverse problems;
  • Radiocommunications signals;
  • Wavelet differentiation;
  • Wavelet thresholding

Summary.  Radio scientists require estimates of the rate of change in rain-induced signals. Unfortunately, these signals are observed in the presence of atmospheric noise, which has a variance that is dependent on temperature, pressure and other climatic variables. We develop a systematic approach to the problem, using wavelet differentiation combined with coefficient-dependent thresholding, and illustrate the considerable benefits that this provides over more conventional techniques.