Abstract: Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or compressible signals.
Abstract: A fast and exact algorithm is developed for the spin \(\pm2\) spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform.
Abstract: A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order \(O(L^5)\), where \(2L\) stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the signals and filters considered.