NEURAL-NETWORK AND WAVELET TRANSFORM FOR SCALE-INVARIANT DATA CLASSIFICATION

Given an astrophysical observation with an arbitrary carrier frequency and an unknown scale under an additive white noise, s'(t)=-s(at)+n (t), its wavelet transform is W'(a,b) - (s'(t),h(ab)(t)), as computed by the inner product with a daughter wavelet h(ab)(t)=h((t -b)/a)/a. W'(a b) equals the original transform W(a,b)=(s(t),h(ab)(t)) displaced along the radial direction W'(a,b)=W(aa,ab) plus noise in the time-scale joint-representation plane. A bank of wedge-shaped detectors collects those displaced transforms W'(a,b) to create a set of invariant features. These features are fed into a two-layer feed-forward artificial neural network, to interpolate discrete sampling, as demonstrated successfully for real-time-signal automatic classification. Useful wavelet applications in turbulence onset, spectrum analyses, fractal aggregates, and bubble-chamber particle-track pattern-recognition problems are indicated but are modeled, in the interest of simplicity, in a one-dimensional example.