The extended Kalman filter (EKF) is considered one of the most effective methods for both nonlinear state estimation and parameter estimation (e.g., learning the weights of a neural network). Recently, a number of derivative free alternatives to the EKF for state estimation have been proposed. These include the Unscented Kalman Filter (UKF) [1, 2], the Central Difference Filter (CDF) [3] and th...

An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis. Abstract. An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our quadrature is als...

This paper details the development of the weak form formulations of finite element type methods using wavelets as basis functions. Such approaches are different from most wavelets based ones that are derived from the strong form. The advantages of the proposed formulation are that there is no need to enforce natural boundary conditions and that the lower order derivatives of the wavelet bases a...

This report proposes a new wavelet–based approach to solving the edge detection problem. The proposed scheme adopts Canny’s three criteria [3] as a guide to derive a wavelet–style edge filter such that the edge points of an image can be detected efficiently and accurately at different scales. Since Canny’s criteria are suitable for those edge detectors that detect local extremes, the desired wa...

This paper considers the design of the WSS paraunitary filterbanks composed of a single complex allpass filter and gives a new class of real-valued orthonormal symmetric wavelet bases. First, the conditions that the complex allpass filter has to satisfy are derived from the symmetry and orthonormality conditions of wavelets, and its transfer function is given to satisfy these conditions. Second...

Recently √ 5-refinement hierarchical sampling has been studied and √ 5-refinement has been used for surface subdivision. Compared with other refinements such as the dyadic or quincunx refinement, √ 5-refinement has a special property that the nodes in a refined lattice form groups of five nodes with these five nodes having different x and y coordinates. This special property has been shown to b...

In this paper, we present a novel method, which uses non-separable wavelet filter banks, to extract the features of texture images for texture image retrieval. Compared to traditional tensor product wavelets (such as db wavelets), our new method can capture more direction and edge information of texture images, which is highly valuable to reflect the essential properties of the texture images. ...

In this paper, we have proposed a tunable two dimensional (2D) photonic crystal (PhC) channel drop filter (CDF) using ring resonators with suitable quality factor (Q) and transmission efficiency; we investigate parameters which have an effect on resonant wavelength in this CDF, such as dielectric constant of inner, coupling, adjacent and whole rods of the structure. Dropping efficiency at the r...

We present constructions of biorthogonal wavelets and associated filter banks with optimality using pseudoframes for subspaces (PFFS). PFFS extends the theory of frames in that pseudoframe sequences need not reside within the subspace of interest. In particular, when PFFS is applied to biorthogonal wavelets the underlying flexibility presents opportunities to incorporate optimality, regularity ...

When bivariate filter banks and wavelets are used for surface multiresolution processing, it is required that the decomposition and reconstruction algorithms for regular vertices derived from them have high symmetry. This symmetry requirement makes it possible to design the corresponding multiresolution algorithms for extraordinary vertices. Recently lifting-scheme based biorthogonal bivariate ...