논문 상세정보
Slepian Spatial-Spectral Concentration Problem on the Sphere: Analytical Formulation for Limited Colatitude–Longitude Spatial Region
-
초록
In this paper, we develop an analytical formulation for the Slepian spatial-spectral concentration problem on the sphere for a limited colatitude-longitude spatial region on the sphere, defined as the Cartesian product of a range of positive colatitudes and longitudes. The solution of the Slepian problem is a set of functions that are optimally concentrated and orthogonal within a spatial or spectral region. These properties make them useful for applications where measurements are taken within a spatially limited region of the sphere and/or a signal is only to be analyzed within a region of the sphere. To support localized spectral/spatial analysis, and estimation and sparse representation of localized data in these applications, we exploit the expansion of spherical harmonics in the complex exponential basis to develop an analytical formulation for the Slepian concentration problem for a limited colatitude-longitude spatial region. We also extend the analytical formulation for spatial regions that are comprised of a union of rotated limited colatitude-longitude subregions. By exploiting various symmetries of the proposed formulation, we design a computationally efficient algorithm for the implementation of the proposed analytical formulation. Such a reduction in computation time is demonstrated through numerical experiments. We present illustrations of our results with the help of numerical examples and show that the representation of a spatially concentrated signal is indeed sparse in the Slepian basis.
활용도 분석
-
상세보기
-
원문보기
원문보기
유료 다운로드의 경우 해당 사이트의 정책에 따라 신규 회원가입, 로그인, 유료 구매 등이 필요할 수 있습니다. 해당 사이트에서 발생하는 귀하의 모든 정보활동은 NDSL의 서비스 정책과 무관합니다.
원문복사신청을 하시면, 일부 해외 인쇄학술지의 경우 외국학술지지원센터(FRIC)에서
무료 원문복사 서비스를 제공합니다.
NDSL에서는 해당 원문을 복사서비스하고 있습니다. 위의 원문복사신청 또는 장바구니 담기를 통하여 원문복사서비스 이용이 가능합니다.