OPTIMAL SCALE TRANSLATIONS IN NOISY MEASUREMENT SYSTEMS

In engineering, medicine, biology and agriculture, it is often desired to replace an invasive or slow measurement method, by nondestructive, faster or less expensive methods. The inevitable question is whether the two measurement methods are interchangeable. To answer this question, the common practice is to use linear regression based equations, as scale translation rules. It is shown that this approach is not optimal, when both measurement methods are noisy. Accordingly, a new approach for method comparisons is proposed, by high fidelity translation of the readings taken on the scale of one test, to the scale of another test, and vice verse. The proposed scale translation mode is based on minimizing the sum of squares of the differences between the absolute values of the fast Fourier transform (FFT) series, derived from the readings of the compared measurement methods. Whereas regression methods attempt to find the parameters of a line that provides the best fit to the observed data pairs, the FFT equalization method strives to find the parameters of a line that can render the difference between the translated readings as close to zero as possible. The line taken is illustrated by a comparative study on several artificial datasets of linearly related paired X, Y readings, with various levels of measurement noise. Quality criteria were developed for quantitative comparison of linear regression based, scale translation models versus the new method, while using the results from the artificially generated datasets for illustration. The comparisons indicate that scale translation by the FFT equalization method is optimal in terms of these quality indexes.