IEEE Trans Image Process - Steerable pyramids and tight wavelet frames in L2(R(d)).

Tópicos

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Resumo

We present a functional framework for the design of tight steerable wavelet frames in any number of dimensions. The 2-D version of the method can be viewed as a generalization of Simoncelli's steerable pyramid that gives access to a larger palette of steerable wavelets via a suitable parametrization. The backbone of our construction is a primal isotropic wavelet frame that provides the multiresolution decomposition of the signal. The steerable wavelets are obtained by applying a one-to-many mapping (Nth-order generalized Riesz transform) to the primal ones. The shaping of the steerable wavelets is controlled by an M?M unitary matrix (where M is the number of wavelet channels) that can be selected arbitrarily; this allows for a much wider range of solutions than the traditional equiangular configuration (steerable pyramid). We give a complete functional description of these generalized wavelet transforms and derive their steering equations. We describe some concrete examples of transforms, including some built around a Mallat-type multiresolution analysis of L(2)(R(d)), and provide a fast Fourier transform-based decomposition algorithm. We also propose a principal-component-based method for signal-adapted wavelet design. Finally, we present some illustrative examples together with a comparison of the denoising performance of various brands of steerable transforms. The results are in favor of an optimized wavelet design (equalized principal component analysis), which consistently performs best.

Resumo Limpo

present function framework design tight steerabl wavelet frame number dimens d version method can view general simoncelli steerabl pyramid give access larger palett steerabl wavelet via suitabl parametr backbon construct primal isotrop wavelet frame provid multiresolut decomposit signal steerabl wavelet obtain appli onetomani map nthorder general riesz transform primal one shape steerabl wavelet control mm unitari matrix m number wavelet channel can select arbitrarili allow much wider rang solut tradit equiangular configur steerabl pyramid give complet function descript general wavelet transform deriv steer equat describ concret exampl transform includ built around mallattyp multiresolut analysi lrd provid fast fourier transformbas decomposit algorithm also propos principalcomponentbas method signaladapt wavelet design final present illustr exampl togeth comparison denois perform various brand steerabl transform result favor optim wavelet design equal princip compon analysi consist perform best

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