In this chapter, I give some background to inversion techniques, especially as they relate to geophysical signal processing. Although the literature concerning inversion and signal processing is vast, some common references to inversion as applied to geophysical signal processing may be found in Webster 1978, Robinson and Treitel 1980, Kanasewich 1981, Tarantola 1987, Menke 1989, Claerbout 1992a, Parker 1994, and Claerbout 1995. Some more general references on inversion of linear systems may be found in Strang 1986, Strang 1988, and Golub and Van Loan 1989. Another goal of this chapter is to give the reader a feeling for the calculation and use of prediction-error filters both in standard filtering applications and in inversion for signal and noise separation, where the prediction-error filters, also referred to here as annihilation filters, characterize signal and noise.
-- methods and problems