We present spatial-Slepian transform~(SST) for the representation of signals on sphere to support localized signal analysis. use well-optimally concentrated Slepian functions, obtained by solving spatial-spectral concentration problem finding bandlimited and spatially optimally functions sphere, formulate proposed transform obtain joint domain signal. Due optimal energy in spatial domain, allow...

The singular value decomposition going with many problems in medical imaging, non-destructive testing, geophysics, is of central importance. Unfortunately the effective numerical determination functions question a very ill-posed problem. best known remedy to this problem goes back work D. Slepian, H.Landau and H. Pollak, Bell Labs 1960-1965. We show that master symmetries Korteweg-de Vries equa...

This work presents the construction of a novel spherical wavelet basis designed for incomplete datasets, i.e. datasets which are missing in particular region sphere. The eigenfunctions Slepian spatial-spectral concentration problem (the functions) set orthogonal functions more concentrated within defined region. allow one to compute convolution on sphere by leveraging recently proposed sifting ...

We consider the problem of (almost) lossless source coding two correlated memoryless sources using separate encoders and a joint decoder, that is, Slepian-Wolf (S-W) coding. In our setting, encoding decoding are asynchronous, i.e., there is certain relative delay between sources. Neither parameters nor known to decoder. Since we assume both implement standard random binning, which does not requ...

The d-dimensional Slepian Gaussian random field {S(t), t ∈ R+} is a mean zero Gaussian process with covariance function ES(s)S(t) = ∏d i=1 max(0, ai − |si − ti|) for ai > 0 and t = (t1, · · · , td) ∈ R+. Small ball probabilities for S(t) are obtained under the L2-norm on [0, 1]d, and under the sup-norm on [0, 1]2 which implies Talagrand’s result for the Brownian sheet. The method of proof for t...