16 accepted papers
We formulate and generalize a sampling scheme on the sphere based on the Gauss-Legendre (GL) quadrature that permits the accurate computation of the spherical harmonic transform (SHT) and its inverse for the signals band-limited at L and order-limited at M using L(2M + 1) number of samples. Signals…
We present an operator formulation for linear transformations in the joint spatial-Slepian domain, which is enabled by the spatial-Slepian transform. The operator is an integral type and is specified by the spatial-Slepian transformation kernel, which is also utilized in finding a matrix representat…
The depletion and variations of groundwater storage (GWS) are of critical importance for sustainable groundwater management. In this work, we use Gravity Recovery and Climate Experiment (GRACE) to estimate variations in the terrestrial water storage (TWS) and use it in conjunction with the Global La…
We present the optimal design of an azimuthally symmetric window signal for carrying out joint spatial-spectral domain filtering of a spherical (source) signal contaminated by a realization of an anisotropic noise process. The resulting window is used in the computation of spatially localized spheri…
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 propose an antipodally symmetric sampling scheme of optimal dimensionality for the sampling of band-limited signals. The proposed scheme takes ~L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> number of samples for the sampling of spherical…
We construct an overcomplete and multiscale dictionary of bandlimited Slepian functions on the sphere. Slepian functions are the bandlimited eigenfunctions obtained by solving spatial-spectral concentration problem on the sphere. To this end, we develop the hierarchical equal area iso-latitude iso-l…
In practice, the finite number of samples of the spherical radiation pattern or antenna gain are taken on the sphere for both the reconstruction of the antenna radiation pattern and the computation of mobile handset performance measures such as directivity and mean effective gain (MEG). The acquisit…
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…