Introduction - Spectral Analysis of Signals: The Missing Data Case - page 5

Following the filter design framework introduced in Chapter 2, GAPES
is developed to iteratively interpolate the missing data and to estimate the
spectrum. A two-dimensional extension of GAPES is also presented.
Chapter 4: In this chapter, we introduce a maximum likelihood (ML) based in-
terpretation of APES. This framework will lay the ground for the general
missing-data problem discussed in the following chapters.
Chapter 5: Although GAPES performs quite well for gapped data, it does not work
well for the more general problem of missing samples occurring in arbitrary
patterns. In this chapter, we develop two MAPES algorithms by using a “ML
fitting” criterion as discussed in Chapter 4. Then we use the well-known
expectation maximization (EM) method to solve the so-obtained estimation
problem iteratively. We also demonstrate the advantage of MAPES-EM over
GAPES by comparing their design approaches.
Chapter 6: Two-dimensional extensions of the MAPES-EM algorithms are devel-
oped. However, because of the high computational complexity involved, the
direct application of MAPES-EM to large data sets, e.g., two-dimensional
data, is computationally prohibitive. To r educe the computational complex-
ity, we develop another MAPES algorithm, referred to as MAPES-CM,
by solving a “ML fitting” problem iteratively via cyclic maximization (CM).
MAPES-EM and MAPES-CM possess similar spectral estimation perfor-
mance, but the computational complexity of the latter is much lower than
that of the former.
Chapter 7: We summarize the topic and provide some concluding remarks. Addi-
tional online resources such as Matlab codes that implement the missing-data
algorithms are also provided.