IEEE Trans Image Process - Wavelet variance analysis for random fields on a regular lattice.

Tópicos

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Resumo

There has been considerable recent interest in using wavelets to analyze time series and images that can be regarded as realizations of certain 1-D and 2-D stochastic processes on a regular lattice. Wavelets give rise to the concept of the wavelet variance (or wavelet power spectrum), which decomposes the variance of a stochastic process on a scale-by-scale basis. The wavelet variance has been applied to a variety of time series, and a statistical theory for estimators of this variance has been developed. While there have been applications of the wavelet variance in the 2-D context (in particular, in works by Unser in 1995 on wavelet-based texture analysis for images and by Lark and Webster in 2004 on analysis of soil properties), a formal statistical theory for such analysis has been lacking. In this paper, we develop the statistical theory by generalizing and extending some of the approaches developed for time series, thus leading to a large-sample theory for estimators of 2-D wavelet variances. We apply our theory to simulated data from Gaussian random fields with exponential covariances and from fractional Brownian surfaces. We demonstrate that the wavelet variance is potentially useful for texture discrimination. We also use our methodology to analyze images of four types of clouds observed over the southeast Pacific Ocean.

Resumo Limpo

consider recent interest use wavelet analyz time seri imag can regard realiz certain d d stochast process regular lattic wavelet give rise concept wavelet varianc wavelet power spectrum decompos varianc stochast process scalebyscal basi wavelet varianc appli varieti time seri statist theori estim varianc develop applic wavelet varianc d context particular work unser waveletbas textur analysi imag lark webster analysi soil properti formal statist theori analysi lack paper develop statist theori general extend approach develop time seri thus lead largesampl theori estim d wavelet varianc appli theori simul data gaussian random field exponenti covari fraction brownian surfac demonstr wavelet varianc potenti use textur discrimin also use methodolog analyz imag four type cloud observ southeast pacif ocean

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