Data reduction by exploiting statistical dependence

It is possible to minimize storage space and processing time requirements for the statistical analysis of multivariate data sets. The data set must first be ergodic so that ensemble averages can be substituted for time averages. Second, there must be some measure indicating that the information carrying capacity of the unit of data storage exceeds the amount of information actually being conveyed. These ideas are explored using a digitized satellite image generated by Landsat 3's multispectral scanner (MSS).

The standard MSS image is represented by a 3240 by 2340 array of picture elements (pixels). However, for each pixel the spectral radiance of four regions of the electromagnetic spectrum are recorded on separate channels. The MSS image can be considered as a very large array whose elements are four-dimensional vectors, thus we can develop an axiomatic basis for defining it as a random field where every element is a random variable. Hence, the principles of random process theory and linear algebra can be applied.

A discrete measure of the information content of each channel shows that the carrying capacity of the unit of storage far exceeds its information content. The transform method of principal components is chosen due to its high degree of efficiency and its ease of implementation on a digital computer. In this case, the result is a single component of data that lacks the detail needed for visual interpretation, but does contain 95% of the variance found within the original four channel data set.