Compressing 3D Measurement Data Under Interval Uncertainty

Abstract

The existing image and data compression techniques try to minimize the mean square deviation between the original data f(x,y,z) and the compressed-decompressed data $\widetilde f(x,y,z)$. In many practical situations, reconstruction that only guaranteed mean square error over the data set is unacceptable.

For example, if we use the meteorological data to plan a best trajectory for a plane, then what we really want to know are the meteorological parameters such as wind, temperature, and pressure along the trajectory. If along this line, the values are not reconstructed accurately enough, the plane may crash – and the fact that on average, we get a good reconstruction, does not help.

In general, what we need is a compression that guarantees that for each (x,y), the difference $|f(x,y,z)-\widetilde f(x,y,z)|$ is bounded by a given value Δ – i.e., that the actual value f(x,y,z) belongs to the interval

$$[\widetilde f(x,y,z)-\Delta,\widetilde f(x,y,z)+\Delta].$$

In this paper, we describe new efficient techniques for data compression under such interval uncertainty.