Number Of Wavelet Coefficients Research Articles

Wavelet-Based Sequential Monte Carlo Blind Receivers in Fading Channels With Unknown Channel Statistics

Recently, an adaptive Bayesian receiver for blind detection in flat-fading channels was developed by the present authors, based on the sequential Monte Carlo methodology. That work is built on a parametric modeling of the fading process in the form of a state-space model and assumes the knowledge of the second-order statistics of the fading channel. In this paper, we develop a nonparametric approach to the problem of blind detection in fading channels, without assuming any knowledge of the channel statistics. The basic idea is to decompose the fading process using a wavelet basis and to use the sequential Monte Carlo technique to track both the wavelet coefficients and the transmitted symbols. A novel resampling-based wavelet shrinkage technique is proposed to dynamically choose the number of wavelet coefficients to best fit the fading process. Under such a framework, blind detectors for both flat-fading channels and frequency-selective fading channels are developed. Simulation results are provided to demonstrate the excellent performance of the proposed blind adaptive receivers.

Wavelets applied to simplification of digital terrain models

Wavelet thresholding is used to generate simplified terrain models. This non-linear filtering technique is adaptive in the sense that the large wavelet coefficients in areas of high relief are kept, whereas all coefficients smaller than a threshold value, representing smooth areas, are thrown away. The degree of detail in the simplified model is controlled by the number of wavelet coefficients retained. Two different areas are analysed using this method. The experiments show the smoothing effect of the thresholding, and how the main terrain features survive as the threshold value increases. At large threshold values the method introduces blocking artifacts in the model.

Nonparametric adaptive detection in fading channels based on sequential Monte Carlo and Bayesian model averaging

Recently, a Bayesian receiver for blind detection in fading channels has been proposed by Chen, Wang and Liu (200,IEEE Trans. Inform. Theory,46, 2079–2094), based on the sequential Monte Carlo methodology. That work is built on a parametric modelling of the fading process in the form of a state-space model, and assumes the knowledge of the second-order statistics of the fading channel. In this paper, we develop a nonparametric approach to the problem of blind detection in fading channels, without assuming any knowledge of the channel statistics. The basic idea is to decompose the fading process using a wavelet basis, and to use the sequential Monte Carlo technique to track both the wavelet coefficients and the transmitted symbols. Moreover, the algorithm is adaptive to time varying speed/smoothness in the fading process and the uncertainty on the number of wavelet coefficients (shrinkage order) needed. Simulation results are provided to demonstrate the excellent performance of the proposed blind adaptive receivers.

An Efficient Adaptive Wavelet-Collocation Method Using Lifted Interpolating Wavelets

The wavelet theory is relatively a new development and now acquires popularity and much interest in many areas including mathematics and engineering. This work presents an adaptive wavelet method for a numerical solution of partial differential equations in a collocation sense. Due to the multi-resolution nature of wavelets, an adaptive strategy can be easily realized it is easy to add or delete the wavelet coefficients as resolution levels progress. Typical wavelet-collocation methods use interpolating wavelets having no vanishing moment, but we propose a new wavelet-collocation method on modified interpolating wavelets having 2 vanishing moments. The use of the modified interpolating wavelets obtained by the lifting scheme requires a smaller number of wavelet coefficients as well as a smaller condition number of system matrices. The latter property makes a preconditioned conjugate gradient solver more useful for efficient analysis.

Geophysical Field Modelling by Multiresolution Analysis

Wavelet transform originated in 1980’s for the analysis of seismic signals has seen an explosion of applications in geophysics. However, almost all of the material is based on wavelets over Euclidean spaces. This paper deals with the generalization of the theory and algorithmic aspects of wavelets to a spherical earth’s model and geophysically relevant vector fields such as the gravitational, magnetic, elastic field of the earth. A scale discrete wavelet approach is considered on the sphere thereby avoiding any type of tensor-valued ‘basis (kernel) function’. The generators of the vector wavelets used for the fast evaluation are assumed to have compact supports. Thus the scale and detail spaces are finite-dimensional. As an important consequence, detail information of the vector field under consideration can be obtained only by a finite number of wavelet coefficients for each scale. Using integration formulas that are exact up to a prescribed polynomial degree, wavelet decomposition and reconstruction are investigated for bandlimited vector fields. A pyramid scheme for the recursive computation of the wavelet coefficients from level to level is described in detail. Finally, data compression is discussed for the EGM96 model of the earth’s gravitational field.