The hexagonal lattice was proposed as an alternative method for image sampling. The hexagonal sampling has certain advantages over the conventionally used square sampling. Hence, the hexagonal lattice has been used in many areas. A hexagonal lattice allows √ 3, dyadic and √ 7 refinements, which makes it possible to use the multiresolution (multiscale) analysis method to process hexagonally samp...

The method of distributions is developed for systems that are governed by hyperbolic conservation laws with stochastic forcing. yields a deterministic equation the cumulative distribution function (CDF) system state, e.g., flow velocity an inviscid Burgers random source coefficients. This achieved without recourse to any closure approximation. CDF model verified against Monte Carlo (MC) simulat...

A new unified method for designing both paraunitary cosine-modulated FIR filter banks and cosine-modulated wavelets is proposed in this paper. This problem has been formulated as a quadratic-constrained least-squares (QCLS) minimization problem in which all constraint matrices are symmetric and positive definite. Furthermore, a specific analog neural network whose energy function is chosen as t...

This paper introduces our recently designed 9/7– 10/8 dual-tree complex filter bank and studies its application in moving object detection and segmentation. The dual-tree complex wavelet transform (DT-CWT) is used in edge detection required for segmentation in video frames. The DT-CWT approach is compared with the previous methods based on scalar wavelets and multi-wavelets (MW), using double c...

In this paper, a design method of two-dimensional (2-D) orthogonal symmetric wavelets is proposed by using a lattice structure for multi-dimensional (M-D) linear-phase paraunitary filter banks (LPPUFB), which the authors have proposed as a previous work and then modified by Lu Gan et al. The derivation process for the constraints on the second-order vanishing moments is shown and some design ex...

Two-dimensional (2-D) compactly supported, orthogonal wavelets and filter banks having linear phase are presented. Two cases are discussed: wavelets with two-fold symmetry (centrosymmetric) and wavelets with four-fold symmetry that are symmetric (or anti-symmetric) about the vertical and horizontal axes. We show that imposing the requirement of linear phase in the case of order-factorable wavel...

THE LAST decade has seen a tremendous amount of activity and emergence of applications in the areas of filter banks and wavelets. These topics are of such wide interest that there have been papers in many different journals, conferences, and workshops in diverse disciplines. However, many aspects of the theory, design, and application of filter banks and wavelets are of great interest to the ci...

This paper addresses a polyphase structure of spectral graph wavelets and filter banks. We consider two-channel critically sampled graph filter banks. In classical signal processing, polyphase structure of filter banks is very useful since downsampler (upsampler) can be placed before analysis filtering (after synthesis filtering). We theoretically derive that a similar structure is also possibl...

Quarry blasts can be effective, low-cost energy sources for seismic imaging, provided that one can deconvolve the extended source signatures produced by ripple firing. This study uses real and synthetic quarry-blast data to compare the performance of several methods for deconvolving mixed-delay signals. The problem considered here is the recovery of the effective source function along a given a...

This thesis addresses the problem of constructing a discrete wavelet approximating the shape of a given pattern. For the design of a biorthogonal wavelet basis we present an approach, which is based on the lifting scheme. The lifting scheme is a parametrisation of all biorthogonal wavelets. It reduces our problem to a linear least squares problem. The special structure of the problem allows for...