CONSTRUCTION OF OVERCOMPLETE MULTISCALE DICTIONARY OF SLEPIAN FUNCTIONS ON THE SPHERE

被引:0
|
作者
Aslam, Adeem [1 ]
Khalid, Zubair [1 ]
机构
[1] Lahore Univ Management Sci, Sch Sci & Engn, Lahore, Pakistan
来源
2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP) | 2019年
关键词
2-sphere; spherical partitioning; spherical harmonics; spatial-spectral concentration; bandlimited signal; SPHEROIDAL WAVE-FUNCTIONS; SPATIOSPECTRAL CONCENTRATION;
D O I
暂无
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
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-longitude pixelization (HEALLPix) scheme for hierarchical partitioning of the sphere into equal area sub-regions called pixels and present its quaternary tree structure. We then solve the concentration problem of finding bandlimited functions with maximal energy concentration in the given spatial region for each pixel and use these spatially concentrated bandlimited functions as dictionary elements. We analyze the span of the dictionary elements and their mutual coherence and show that the dictionary spans the space of bandlimited functions which are optimally (energy) concentrated within a pixel on the sphere with most of its elements exhibiting negligibly small mutual coherence. Hence, the proposed dictionary is a significant tool for use in multi-resolution analysis and sparse reconstruction of signals on the sphere.
引用
收藏
页码:5137 / 5141
页数:5
相关论文
共 50 条
  • [1] Overcomplete Multiscale Dictionary of Slepian Functions for HEALPix on the Sphere
    Aslam, Adeem
    Khalid, Zubair
    IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2023, 71 : 2532 - 2547
  • [2] Fast Overcomplete Dictionary Construction with Probabilistic Guarantees
    Au-Yeung, Enrico
    Zanotti, Greg
    BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2020, 51 (03): : 719 - 743
  • [3] Fast Overcomplete Dictionary Construction with Probabilistic Guarantees
    Enrico Au-Yeung
    Greg Zanotti
    Bulletin of the Brazilian Mathematical Society, New Series, 2020, 51 : 719 - 743
  • [4] A unified approach to scalar, vector, and tensor Slepian functions on the sphere and their construction by a commuting operator
    Michel, V
    Plattner, A.
    Seibert, K.
    ANALYSIS AND APPLICATIONS, 2022, 20 (05) : 947 - 988
  • [5] Efficient Computation of Slepian Functions for Arbitrary Regions on the Sphere
    Bates, Alice P.
    Khalid, Zubair
    Kennedy, Rodney A.
    IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2017, 65 (16) : 4379 - 4393
  • [6] Slepian functions on the sphere, generalized Gaussian quadrature rule
    Miranian, L
    INVERSE PROBLEMS, 2004, 20 (03) : 877 - 892
  • [7] ANALYSIS OF REAL VECTOR FIELDS ON THE SPHERE USING SLEPIAN FUNCTIONS
    Plattner, Alain
    Simons, Frederik J.
    Wei, Liying
    2012 IEEE STATISTICAL SIGNAL PROCESSING WORKSHOP (SSP), 2012, : 1 - 4
  • [8] Band-limited functions on a bounded spherical domain:: the Slepian problem on the sphere
    Albertella, A
    Sansò, F
    Sneeuw, N
    JOURNAL OF GEODESY, 1999, 73 (09) : 436 - 447
  • [9] On the use of Slepian Functions for the Reconstruction of the Head-Related Transfer Function on the Sphere
    Bates, Alice P.
    Khalid, Zubair
    Kennedy, Rodney A.
    2015 9TH INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING AND COMMUNICATION SYSTEMS (ICSPCS), 2015,
  • [10] Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere
    A. Albertella
    F. Sansò
    N. Sneeuw
    Journal of Geodesy, 1999, 73 : 436 - 447