Wavelets for Statistical Estimation and Detection
R. Chandramouli, Kandethody M. Ramachandran · Birkhäuser Boston eBooks · 2003
In this chapter, we discuss two important statistical applications of wavelets: (a) signal estimation and (b) signal detection. Several popular wavelet-based signal estimation/de-noising schemes are reviewed, followed by the introduction of a new signal estimator that attempts to estimate and preserve some moments of the underlying original signal. A relationship between signal estimation and data compression is also discussed. Analytical and experimental results are presented to explain the performance of these signal estimation schemes. The second part of this chapter deals with hypothesis testing-based signal detection. Wavelet decomposition level-dependent binary hypothesis tests are first presented, followed by global detection procedures that combine these decisions to obtain the final decision. Likelihood ratio-based statistical detectors are discussed toward this goal. The combinatorial explosion of the global detector design results in the investigation of two specific global detection fusion rules: OR and AND. Some mathematical approximations are exploited that aid in trading off complexity for the global detector performance. Theorems and their proofs relating to this issue are presented. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.