Space-frequency balance in biorthogonal wavelets

Abstract

ABSTRACT

A new approach to design triplet halfband filter banks based on balanced-uncertainty optimization

“…In [20], the better performance of image compression algorithms is shown by balancing time and frequency localizations of wavelet filters. In pioneering work [21], Tay introduced an optimization of a balanceduncertainty (BU) metric [20] using PBP to design a class of HPFB [5]. The designed filters have good balance of time-frequency localizations.…”

“…It has been addressed in [19][20][21][22][23] that the optimal FBs designed to achieve different balance between the time and frequency localizations are very effective in image compression, image segmentation and feature extraction algorithms. Moreover, the timefrequency localized optimization criteria has been used in the design of optimal HPFB.…”

Balanced-Uncertainty Optimized Wavelet Filters with Prescribed Vanishing Moments

“…In this paper, we use a criterion that represents a balance between time localization and frequency localization. The criterion was proposed by Monro [5], [6] and is called the Heisenberg balanced-uncertainty (BU) metric. For a filter with impulse response h(n)(and frequency response H (ω)), the metric is defined as…”

“…However, with the BU metric, the relative importance of the time and frequency localizations, which may be signal and application dependent, can be controlled through the footprint constant k. This metric was used in [5] and [6] to design wavelet filters that performed well in image compression application. A fairly complex, constrained optimization design process was used in [5] and [6]. But no general vanishing moments constraints was imposed in [5] and [6] (only a simple zero).…”

“…A fairly complex, constrained optimization design process was used in [5] and [6]. But no general vanishing moments constraints was imposed in [5] and [6] (only a simple zero). The BU metric per se does not have any physical significance, but it provides a simple way to trade off time localization with frequency localization in wavelet design.…”