To separate signal and noise in the presence of high-amplitude noise, the worst of the high-amplitude noise should be removed to avoid crippling the least-squares inversion. In chapter , a method for eliminating high-amplitude noise is demonstrated. In this chapter, an inversion that predicts missing data while it separates signal and noise is presented. This inversion is a modification of the inversion used in the previous chapter. Although missing data far from the known data is not well predicted, most of the missing data have been restored with reasonable success. The signal and the noise have also been separated successfully.
When removing random noise, the process of predicting missing data and the process of separating signal and noise are likely to give similar answers when performed either separately or simultaneously. There is a practical advantage, since the cost of doing a single inversion is likely to be less than two inversions. Coherent noise will require the simultaneous calculation of the missing data with the calculation of the signal or noise. In the next chapters, I will extend these inversions to use not only a signal filter, but to use filters describing the noise also.