Scale and Translation Invariant Methods for Enhanced Time-Frequency Pattern Recognition

Abstract

Time-frequency (t-f) analysis has clearly reached a certain maturity. One can now often provide striking visual representations of the joint time-frequency energy representation of signals. However, it has been difficult to take advantage of this rich source of information concerning the signal, especially for multidimensional signals. Properly constructed time-frequency distributions enjoy many desirable properties. Attempts to incorporate t-f analysis results into pattern recognition schemes have not been notably successful to date. Aided by Cohen's scale transform one may construct representations from the t-f results which are highly useful in pattern classification. Such methods can produce two dimensional representations which are invariant to time-shift, frequency-shift and scale changes. In addition, two dimensional objects such as images can be represented in a like manner in a four dimensional form. Even so, remaining extraneous variations often defeat the pattern classification approach. This paper presents a method based on noise subspace concepts. The noise subspace enhancement allows one to separate the desired invariant forms from extraneous variations, yielding much improved classification results. Examples from sound classification are discussed.