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What is a Prolate Spheroid wave function?

  1. Jul 6, 2015 #1
    What is a Prolate Spheroid Wave Function and how does it apply to EEGs and brain mapping ?


    Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and band-limit

    http://www.sciencedirect.com/science/article/pii/S1063520306000650
    https://upload.wikimedia.org/wikipe...eroidCoord.png/360px-ProlateSpheroidCoord.png



    http://www.researchgate.net/publication/251973013_Discrete_Prolate_Spheroidal_Sequences_for_compressive_sensing_of_EEG_signals [Broken]

    Dissociating neuronal gamma-band activity from cranial and ocular muscle activity in EEG
    http://journal.frontiersin.org/article/10.3389/fnhum.2013.00338/full
    (seems like they are trying to reduce the amount of "noise" using PSWF, focusing in on the EEG nodes by only capturing the wave function of the human head???? is this right ?)


    If the prolate spheroid is a better and more accurate model of the human head and the wave-function of a prolate spheroid is being sought/ used, is the wave-function of a brain then being utilized with this "medical" technology ?


    Could this be a method of data acquisition for mind uploading/ brain mapping ?


    Human Brain Mapping 29:1276–1287 (2008)
    Spatial Smoothing in fMRI Using Prolate
    Spheroidal Wave Functions
    http://wagerlab.colorado.edu/files/papers/Lindquist_2008_Hum%20Brain%20Mapp.pdf [Broken]



    is data acquisition the reason they are using the wave-function of a prolate spheroid ?
    because..


    & Might it be possible to combine the PSWF method with this wave-function measurement method ?
    http://www.rochester.edu/newscenter...que-efficiently-finds-quantum-wave-functions/



    both DO seem to deal with data acquisition and reconstruction techniques....
    AND.. both "COMPRESSIVE DIRECT MEASUREMENT" and "COMPRESSIVE SENSING" are used...
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Jul 7, 2015 #2

    DrDu

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    Science Advisor

    Prolate and oblate spheroidal refers to the shape of a 3D elipsoid. In the prolate case it is streched along one axis, in the oblate case, it is flattened.
    Some differential equations can be separated in a prolate spheroidal coordinate system. One coordinate is the rotation angle phi, the other two are generalizations of the radius (mu) and angle (nu) in the spherical case.
    In contrast to the spherical case, the surfaces mu=const are elipsoids (and not spheres) and the surfaces corresponding to vu=const are hyperbola (not cones), like in one of the pictures you shew.
     
    Last edited: Jul 7, 2015
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