What is a Prolate Spheroid wave function?

[Checkster2323]

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

A prolate spheroid of variable eccentricity is used to provide a more accurate model of the geometry of the human head than is possible with a simple sphere.

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

In this paper we show that using Discrete Prolate Spheroidal Sequences, rather than sine functions, it is possible to derive a sampling and reconstruction method which is similar to CS.
Assuming non-uniform sampling our procedure can be connected with compressive sensing without complex reconstruction methods.
Discrete Prolate Spheroidal Sequences for compressive sensing of EEG signals- ResearchGate. Available from:http://www.researchgate.net/publication/251973013_Discrete_Prolate_Spheroidal_Sequences_for_compressive_sensing_of_EEG_signals [accessed Jun 22, 2015].

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 ?

The focus of mind uploading, in the case of copy-and-transfer, is on data acquisition

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

The result of every possible measurement on a quantum system is coded in its wave function,

& 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/

The new method, called compressive direct measurement,allowed the team to reconstruct a quantum state at 90 percent fidelity(a measure of accuracy) using only a quarter of the measurements required by previous methods.

both DO seem to deal with data acquisition and reconstruction techniques...
AND.. both "COMPRESSIVE DIRECT MEASUREMENT" and "COMPRESSIVE SENSING" are used...

 

[DrDu]

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.