Discrete wavelet transform-based RI adaptive algorithm for system identification

In this paper, we propose a new adaptive filtering algorithm for system identification. The algorithm is based on the recursive inverse (RI) adaptive algorithm which suffers from low convergence rates in some applications; i.e., the eigenvalue spread of the autocorrelation matrix is relatively high. The proposed algorithm applies discrete-wavelet transform (DWT) to the input signal which, in turn, helps to overcome the low convergence rate of the RI algorithm with relatively small step-size(s). Different scenarios has been investigated in different noise environments in system identification setting. Experiments demonstrate the advantages of the proposed DWT recursive inverse (DWT-RI) filter in terms of convergence rate and mean-square-error (MSE) compared to the RI, discrete cosine transform LMS (DCTLMS), discrete-wavelet transform LMS (DWT-LMS) and recursive-least-squares (RLS) algorithms under same conditions

European Equity Market Integration and Optimal Investment Horizons – Evidence from Wavelet Analysis

In the paper the process of equity market integration in Europe is examined from the wavelet perspective. The method applied is the Continuous Discrete Wavelet Transform that enables to perform global and local wavelet variance and correlation decompositions. In particular, questions about changes of the investment risk and the possibility of international portfolio diversification under different investment horizons are addressed. The study documents both convergence of the Central and Eastern European equity markets as well as their segmentation on the European market. The latter enables reduction of portfolio returns variability by an international portfolio diversification, especially for long investment horizons.equity market integration, time-scale analysis, wavelet variance, wavelet correlations.

Signal recovery from wavelet transform maxima

Cataloged from PDF version of article.This paper presents an iterative algorithm for signal recovery from discrete-time wavelet transform maxima. The signal recovery algorithm is developed by using the method of projections onto convex sets. Convergence of the algorithm is assured

Fast Compressed Sensing MRI Based on Complex Double-Density Dual-Tree Discrete Wavelet Transform

Compressed sensing (CS) has been applied to accelerate magnetic resonance imaging (MRI) for many years. Due to the lack of translation invariance of the wavelet basis, undersampled MRI reconstruction based on discrete wavelet transform may result in serious artifacts. In this paper, we propose a CS-based reconstruction scheme, which combines complex double-density dual-tree discrete wavelet transform (CDDDT-DWT) with fast iterative shrinkage/soft thresholding algorithm (FISTA) to efficiently reduce such visual artifacts. The CDDDT-DWT has the characteristics of shift invariance, high degree, and a good directional selectivity. In addition, FISTA has an excellent convergence rate, and the design of FISTA is simple. Compared with conventional CS-based reconstruction methods, the experimental results demonstrate that this novel approach achieves higher peak signal-to-noise ratio (PSNR), larger signal-to-noise ratio (SNR), better structural similarity index (SSIM), and lower relative error

European Equity Market Integration and Optimal Investment Horizons – Evidence from Wavelet Analysis

In the paper the process of equity market integration in Europe is examined from  the wavelet perspective. The method applied is the Continuous Discrete Wavelet Transform that  enables to perform global and local wavelet variance and correlation decompositions. In particular,  questions about changes of the investment risk and the possibility of international portfolio  diversification under different investment horizons are addressed. The study documents both  convergence of the Central and Eastern European equity markets as well as their segmentation on  the European market. The latter enables reduction of portfolio returns variability by an international  portfolio diversification, especially for long investment horizons.

Robust Estimation and Wavelet Thresholding in Partial Linear Models

This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We present a wavelet thresholding based estimation procedure to estimate the components of the partial linear model by establishing a connection between an $l_1$-penalty based wavelet estimator of the nonparametric component and Huber's M-estimation of a standard linear model with outliers. Some general results on the large sample properties of the estimates of both the parametric and the nonparametric part of the model are established. Simulations and a real example are used to illustrate the general results and to compare the proposed methodology with other methods available in the recent literature

Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes

This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of any given path of the $M$-band wavelet packet decomposition tree. It is shown that if the input process is centred and strictly stationary, these sequences converge in distribution to white Gaussian processes when the resolution level increases, provided that the decomposition filters satisfy a suitable property of regularity. For any given path, the variance of the limit white Gaussian process directly relates to the value of the input process power spectral density at a specific frequency.Comment: Submitted to the IEEE Transactions on Signal Processing, October 200