Construction of an orthonormal complex multiresolution analysis

Abstract

We design two complex filters {h[n], g[n])} for an orthogonal filter bank structure based on two atom functions {ρ₀^α(t), ρ_1/2^α(t)}, such that: 1) they generate an orthonormal multiwavelet basis; 2) the two complex conjugate wavelets are Hilbert wavelets, i.e., their frequency responses are supported either on positive or negative frequencies; and 3) the two scaling functions are real. The developed complex wavelet transform (CWT) is non-redundant, nearly shift-invariant, and distinguishable for diagonal features. The distinguishability in diagonal features is demonstrated by comparison with real discrete wavelet transform.