Definitions

In this section, the terms needed to describe the inversion are defined. First, it is assumed that a signal annihilation filter $\st S$is available. When applied to the signal $\sv s$, the signal is eliminated to a good approximation: $\st S \sv s \approx \sv 0$. The filter $\st S$ is a purely lateral prediction filter as described in chapter  and is calculated in the same way as the $\st S$ in chapter . The data $\sv d$ is assumed to be the sum of signal $\sv s$ and noise $\sv n$,or $\sv d=\sv s+\sv n$.The data $\sv d$ is also separated into the data that is known $\sv k$and the data that is missing $\sv m$, so that $\sv d=\sv k+\sv m$.The missing data is the data not recorded or the data that has been eliminated by the high-amplitude noise muting routine presented in the previous section. Two masks are defined for use in the inversion. $\st K$ is the mask, that when applied to the data $\sv d$, generates the known data values: $\sv k = \st K\sv d$.$\st M$ is the mask, that when applied to the data $\sv d$, generates the missing data values: $\sv m=\st M\sv d$.The identity matrix $\st I$ results when $\st K$ and $\st M$ are added: $\st I=\st K+\st M$.

To summarize :
$\sv d$ = data
$\sv s$ = signal
$\sv n$ = noise
$\sv k$ = known data
$\sv m$ = missing data
$\st K$ = known data mask
$\st M$ = missing data mask
$\st S$ = signal annihilation filter.
The relationships between these factors are as follows:
$\st S \sv s \approx \sv 0$
$\sv d=\sv s+\sv n$
$\sv d=\sv k+\sv m$
$\st I=\st K+\st M$ or $\sv d = \st K\sv d + \st M\sv d$.