Multiplicative Propagation of Error During Recursive Wavelet Estimation

TL;DR

This paper investigates how recursive wavelet coefficient estimation accumulates errors at coarser scales, revealing that truncation errors can rapidly compromise the reliability of wavelet analysis.

Contribution

It provides a systematic numerical analysis of error propagation in recursive wavelet estimation, highlighting the impact of quantization and round-off errors.

Findings

Truncation errors grow exponentially at coarser scales

Error propagation can render wavelet results unreliable

Analysis is based on a simple sub-band coding scheme

Abstract

Wavelet coefficients are estimated recursively at progressively coarser scales recursively. As a result, the estimation is prone to multiplicative propagation of truncation errors due to quantization and round-off at each stage. Yet, the influence of this propagation on wavelet filter output has not been explored systematically. Through numerical error analysis of a simple, generic sub-band coding scheme with a half-band low pass finite impulse-response filter for down sampling, we show that truncation error in estimated wavelet filter coefficients can quickly reach unacceptable levels, and may render the results unreliable especially at coarser scales.