In this note we apply some recent results on nonlinear wavelet analysis to image processing. In particular we illustrate how the (soft) thresholding algorithm due to Donoho and Johnstone can successfully be used to remove speckle in SAR imagery. Furthermore, we also show that transform coding artifacts, such as blocking in the JPEG algorithm, can be ...

We propose a hybrid approach to wavelet-based deconvolution that comprises Fourier-domain system inversion followed by wavelet-domain noise suppression. In contrast to other wavelet-based deconvolution approaches, the algorithm employs a <i>regularized inverse filter</i>, which allows it to operate even when the system is non-invertible. Using a ...

We study <i>fractional Brownian motions in multifractal time</i>, a model for multifractal processes proposed recently in the context of economics. Our interest focuses on the statistical properties of the wavelet decomposition of these processes, such as residual correlations (LRD) and stationarity, which are instrumental towards computing the ...

This paper presents results on the multiresolution analysis of nonstationary signals with the objective of detecting underlying periodic phenomena. Wavelet packet analysis with coefficient thresholding is the basis for the detection. The effectiveness of the method is illustrated by analyzing experimental data on sediment electrochemical redox potential ...

Low rank estimators for higher order statistics are considered in this paper. Rank reduction methods offer a general principle for trading estimator bias for reduced estimator variance. The bias-variance tradeoff is analyzed for low rank estimators of higher order statistics using a tensor product formulation for the moments and cumulants. In general ...

In the study of the involved geometry of singular distributions the use of fractal and multifractal analysis has shown results of outstanding significance. So far, the investigation has focused on structures produced by one single mechanism which were analyzed with respect to the ordinary metric or volume. Most prominent examples include self-similar ...

In an earlier paper the authors introduced the <i>inverse measure</i> <i>µ</i>^â(<i>dt</i>) of a given measure <i>µ</i>(<i>dt</i>) on [0,1] and presented the 'inversion formula' <i>f</i>^â(<i>a</i>) = <i>a</i><i>f</i>(1/<i>a</i>) which was argued to link the respective multifractal spectra of <i>µ</i> and <i>µ</i><sup>â ...

In this paper we describe how the theory of wavelet thresholding introduced by Donoho and Johnstone can successfully be applied to two distinct problems in image processing where traditional linear filtering techniques are insufficient. The first application is related to speckle reduction in coherent imaging systems. We show that the proposed method ...

Usual fixed-size box-counting algorithms are inefficient for computing generalized fractal dimensions D(<i>q</i>) in the range of <i>q</i><0. In this Letter we describe a new numerical algorithm specifically devised to estimate generalized dimensions for large negative <i>q</i>, providing evidence of its better performance. We compute the complete ...

This paper evaluates the performance of the recently published wavelet based algorithm for speckle reduction of SAR images. The original algorithm, based on the theory of wavelet thresholding due to Donoho and Johnstone, has been shown to improve speckle statistics. In this paper we give more extensive results based on tests performed at Lincoln ...