Two basic tools of free probability are the R-transform and the S-transform. These transforms were introduced by Voiculescu in the 1980s, and are used to understand the addition and the multiplication of two free random variables respectively. The R-transform has a natural and very useful multi-variable extension describing the addition of two free k-tuples of random variables, but the problem ...

In this paper, we will illustrate the F-transform based on generalized fuzzy partitions as a tool for expectile smoothing. This allows to represent a time series in terms of a fuzzy-valued function whose level-cuts are modeled by F-transform and estimated by expectile regression. The proposed methodology is illustrated on real economic and …nancial time series. Keywords: Fuzzy Transform, Expect...

In the last decade a broad literature has arisen studying sparse recovery, the estimation of sparse vectors from low dimensional linear projections. Sparse recovery has a wide variety of applications such as streaming algorithms, image acquisition, and disease testing. A particularly important subclass of sparse recovery is the sparse Fourier transform, which considers the computation of a disc...

The symmetric spaces the title refers to are the spaces X = G=K where G is a connected semisimple Lie group with nite center and K is a maximal compact subgroup. The Fourier transform on X is deened by means of the Iwasawa decomposition G = NAK of G where N is nilpotent and A abelian. Let g; n; a; k denote the corresponding Lie algebras. We also need the group M = K A ; the centralizer of A in ...

This paper presents an algorithm for medical 3D image denoising and segmentation using redundant discrete wavelet transform. First, we present a two stage denoising algorithm using the image fusion concept. The algorithm starts with globally denoising the brain images (3D volume) using Perona Malik’s algorithm and RDWT based algorithms followed by combining the outputs using entropy based fusio...

A novel method of gender Classification from fingerprint is proposed based on discrete wavelet transform (DWT) and singular value decomposition (SVD). The classification is achieved by extracting the energy computed from all the sub-bands of DWT combined with the spatial features of non-zero singular values obtained from the SVD of fingerprint images. K nearest neighbor (KNN) used as a classifi...

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