9 accepted papers
We propose a method for the accurate and robust reconstruction of the non-bandlimited finite rate of innovation signals on the sphere. For signals consisting of a finite number of Dirac functions on the sphere, we develop an annihilating filter based method for the accurate recovery of parameters of…
We develop an algorithm for the extrapolation of band-limited signals on the sphere. The proposed algorithm improves the accuracy of the extrapolation of band-limited signal by using the information contained in the out-of-band harmonic coefficients of the signal to update the extrapolated signal at…
We propose an iso-latitude sampling scheme for the representation of band-limited signals on the sphere. The proposed scheme is designed as a variant of the widely used Hierarchical Equal Area iso-Latitude Pixelization (HEALPix) scheme on the sphere. We use HEALPix grid of resolution N <sub xmlns:mm…
To support the applications where the measurements can only be taken over spatially limited region on the sphere due to practical limitations, we design a spatially-limited sampling scheme on the sphere for the computation of spherical harmonic transform (SHT) of band-limited signals. By enclosing t…
For the fast and exact computation of spherical harmonic transform (SHT) of a band-limited signal defined on the sphere from its samples, the Gauss-Legendre (GL) and equiangular sampling schemes on the sphere require asymptotically least number of samples. In comparison to the equiangular scheme, th…
We develop a robust method for the accurate reconstruction of non-bandlimited finite rate of innovation signals composed of finite number of Diracs. For the recovery of parameters of K Diracs defining the signal, the proposed method requires more than (K + √K) <sup xmlns:mml="http://www.w3.org/1998/…
We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal symmetry, we design a sampling scheme that requires the optima…
In this work, we design complete orthonormal basis functions, which are referred to as optimal basis functions, that span the vector sum of subspaces formed by band-limited spatially concentrated and space-limited spectrally concentrated functions. The optimal basis are shown to be a linear combinat…
We develop a method to compute spherical harmonic transform (SHT) of a band-limited signal on the sphere discretized over a minimum dimensionality regular sampling grid on the sphere. For the computation of SHT of a signal band-limited at L, the proposed method requires L2 number of samples on a reg…