In this section, the terms needed to describe the inversion are defined. First, it is assumed that a signal annihilation filter is available. When applied to the signal , the signal is eliminated to a good approximation: . The filter is a purely lateral prediction filter as described in chapter and is calculated in the same way as the in chapter . The data is assumed to be the sum of signal and noise ,or .The data is also separated into the data that is known and the data that is missing , so that .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. is the mask, that when applied to the data , generates the known data values: . is the mask, that when applied to the data , generates the missing data values: .The identity matrix results when and are added: .

To summarize :

= data

= signal

= noise

= known data

= missing data

= known data mask

= missing data mask

= signal annihilation filter.

The relationships between these factors are as follows:

or .

2/9/2001