Amplitude bound interpolation of sonic well-log data

The problem of interpolating and resampling signals known to result from the application of a linear operator to signals whose minimum and maximum values are known is addressed. These limits are physically meaningful in many applications, and modeling the signals with the limits is preferable to modeling with the unrealistic energy bounds that are sometimes used. It is shown that these more realistic bounds (called amplitude bounds) induce estimation techniques and estimates which have different properties than the ones induced by energy bounds. This allows, potentially, more accurate signal processing and more accurate design of signal processing systems, when the signals are well-described by these bounds. The energy-bound estimation techniques and estimates are reviewed. It is shown that amplitude-bound estimation may be implemented with a modified linear programming technique