Multiresolution analysis

About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.

Human brain dynamics: the analysis of EEG signals with Tsallis information measure

Abstract: We undertake the study of human EEG-signals by recourse to a wavelet based multiresolution analysis as adapted to an Information-Measure-Scenario. Dierent information measures are employed. It is shown that non-extensive ones seem to be of particular usefulness. Their use opens up perspectives of building up automatic detection devices. Conjectures concerning general characteristics of focal epilepsy are formulated on the basis of a Tsallis-type of analysis. c 1999 Elsevier Science B.V. All rights reserved.

Multiresolution analysis in fMRI: sensitivity and specificity in the detection of brain activation.

Abstract: Multiresolution analysis of fMRI studies using wavelets is a new approach, previously reported to yield higher sensitivity in the detection of activation areas. No data are available, however, in the literature on the analytic approach and wavelet bases that produce optimum results. The present study was undertaken to assess the performance of different wavelet decomposition schemes by making use of a “gold standard,” a realistic computer-simulated phantom. As activation areas are then known ‘a priori,’ accurate assessments of sensitivity, specificity, ROC curve area and spatial resolution can be obtained. This approach has allowed us to study the effect of different factors: the size of the activation area, activity level, signal-to-noise ratio (SNR), use of pre-smoothing, wavelet base function and order and resolution level depth. Activations were detected by performing t-tests in the wavelet domain and constructing the final image from those coefficients that passed the significance test at a given P-value threshold. In contrast to previously reported data, our simulation study shows that lower wavelet orders and resolution depths should be used to obtain optimum results (in terms of ROC curve area). The Gabor decomposition offers the maximum fidelity in preserving activation area shapes. No major differences were found between other wavelet bases functions. Data pre-smoothing increases ROC area for all but very small activation region sizes. Hum. Brain Mapping 14:16–27, 2001. © 2001 Wiley-Liss, Inc.

FBWN: An architecture of fast beta wavelet networks for image classification

Abstract: Image classification is an important task in computer vision. In this paper, we propose a supervised method for image classification based on a fast beta wavelet networks (FBWN) model. First, the structure of the wavelet network is detailed. Then, to enhance the performance of wavelet networks, a novel learning algorithm based on the Fast Wavelet Transform (FWTLA) is proposed. It has many advantages compared to other algorithms, in which we solve the problem of the previous works, when the weights of the hidden layer to the output layer are determinate by applying the back propagation algorithm or by direct solution which requires to compute matrix inversion, this may be intensive computation when the learning data is too large. However, the new algorithm is realized by the iterative application of FWT to compute connection weights. In the simulation part, the proposed method is employed to classify images. Comparisons with classical wavelet network classifier are presented and discussed. Results of comparison have shown that the FBWN model performs better than the previously established model in the context of training run time and classification rate.

Measuring the Galaxy Power Spectrum and Scale-Scale Correlations with Multiresolution-decomposed Covariance. I. Method

Abstract: We present a method for measuring the galaxy power spectrum based on multiresolution analysis of the discrete wavelet transformation (DWT). Apart from the technical advantages of the computational feasibility for data sets with a large volume and complex geometry, the DWT scale-by-scale decomposition provides a physical insight into the covariance matrix of the cosmic mass field. Since the DWT representation has a strong capability for suppressing the off-diagonal components of the covariance for self-similar clustering, the DWT covariance for all popular models of the cold dark matter cosmogony is generally diagonal, or j (scale) diagonal in the scale range in which the second or higher order scale-scale correlations are weak. In this range, the DWT covariance gives a lossless estimation of the power spectrum, which is equal to the corresponding Fourier power spectrum banded with a logarithmical scaling. This DWT estimator is optimized in the sense that the spatial resolution is automatically adaptive to the perturbation wavelength to be studied. In the scale range in which the scale-scale correlation is significant, the accuracy of a power spectrum detection depends on the scale-scale or band-band correlations. In this case, for a precision measurements of the power spectrum, or a precision comparison of the observed power spectrum with models, a measurement of the scale-scale or band-band correlations is needed. We show that the DWT covariance can be employed to measure both the band-power spectrum and second-order scale-scale correlation. We also present the DWT algorithm of the binning and Poisson sampling with real observational data. We show that the so-called alias effect appeared in usual binning schemes can exactly be eliminated by the DWT binning. Since the Poisson process possesses diagonal covariance in the DWT representation, the Poisson sampling and selection effects on the power spectrum and second order scale-scale correlation detection are suppressed into a minimum. Moreover, the effect of the non-Gaussian features of the Poisson sampling can also be calculated in this frame. The DWT method is open, i.e., one can add further DWT algorithms on the basic decomposition in order to estimate other effects on the power spectrum detection, such as non-Gaussian correlations and bias models.