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This repository contains a collection of Matlab routines to accompany the paper Sampling Sparse Signals on the Sphere: Algorithms and Applications by Ivan Dokmanić and Yue M. Lu

Dependecies: This code requires some routines from the Spherical Harmonic Transform package SSHT by Jason McEwen and Yves Wiaux. SSSH can be obtained at this link. Most of these dependencies will be removed in the future.

Main functions

Filename Description
SphereFRI.m Runs the FRI estimation algorithm
DiracSpectrum.m Computes the spectrum of a collection of Diracs
RandomDiracs.m Creates a random collection of spherical Diracs
SphereFRI_SN.m Estimation routine for the shot noise removal
SelectEms.m Selects data matrix elements for some m
LegendreCoeffs.m Coefficients of Legendre polynomials
PolypartCoeffs.m Coefficients of the polynomial part of the spherical harmonic
CramerRaoBound.m Computation of the Cramer Rao lower bound
CmMatrix.m Matrix of polynomial coefficients corresponding to m

Note: The code to generate the spherical harmonics currently can't generate harmonics of high orders (to be replaced soon).

Examples and paper figures

Filename Description
Example1_Diracs.m Simple reconstruction of a collection of Diracs
Example2_Green.m Some plots of the Helmholtz Green's function ove r a rigid sphere
Example4_Green.m Figure 7 from the paper (source localization)
Example5_Green.m Figure 8 from the paper (ratios of Green's functions)
Example6_Diffusion.m Diffusion kernel and aliasing error
Example7_Diffusion.m Diffusion reconstruction example
Example8_ShotNoise.m Shot noise removal example


Ivan Dokmanić is with Laboratory for Audiovisual Communications (LCAV) at EPFL, Switzerland. Yue M. Lu is with Signals, Information, and Networks Group ([SING][]) at Harvard University, Cambridge, MA, USA.