One-Dimensional Missing-Data APES via Expectation Maximization - Spectral Analysis of Signals: The Missing Data Case - page 36

CHAPTER 5

One-Dimensional
Missing-Data APES via
Expectation Maximization

5.1 INTRODUCTION
In Chapter 3 we presented GAPES for gapped-data spectral estimation. GAPES
iteratively interpolates the missing data and estimates the spectrum. However,
GAPES can deal only with missing data occurring in gaps and it does not work
well for the more general problem of missing data samples occurring in arbitrary
patterns.
In this chapter, we consider the problem of nonparametric spectral estima-
tion for data sequences with missing data samples occurring in arbitrary patterns
(including the gapped-data case) [45]. We develop two missing-data amplitude
and phase estimation (MAPES) algorithms by using a “ML” fitting criterion as de-
rived in Chapter 4. Then we use the well-known expectation maximization (EM)
[42, 46] method to solve the so-obtained estimation problem iteratively. Through
numerical simulations, we demonstrate the excellent performance of the MAPES
algorithms for missing-data spectral estimation and missing-data restoration.
The remainder of this chapter is organized as follows: In Section 5.2, we give
abrief review of the EM algorithm for the missing-data problem. In Sections 5.3
and 5.4, we develop two nonparametric MAPES algorithms for the missing-data
spectral estimation problem via the EM algorithm. Some aspects of interest are