Simulation of Interference Projections and Reconstructions


This page shows some first experiments with the H-interference transformation (HIT). Also it demonstrates differences between projection and reconstruction at some practical examples.
(Difference between interferential reconstruction and projection: A projection appears as the natural way to project anything: A photograph, a sensitive map. The result interference integral field appears mirrored in general. Time flows straight forward. We compute the excitement at the destination, the "detector space".
In opposite, reconstruction is the computational way to get the excitment map of the source "field" in nonmirrored form: by negation of the time axis we can calculate back into the source, the "generator field". We compute back in time onto the "generator"-field. We get an approximation in form of a non-mirrored reconstruction.)
The terms "field" or "space" have only a demonstrative function. Each pixle of the "field" is connected direct to all channel origins, the delay of each line is proportional to its length. In other words, we reach a discrete, spherical wave propagation with this arrangement.

Channel Generation: Generator Space to Channel

Supposed, we have neural activity at different places in a neural field (generator field). For example, spiking neurons are black pixels in the following bitmap in form of a 'G'. Supposed further, 30 sensors or electrodes connect this bitmap at "channel origins", numbers 0...29.

Neurons are supposed to fire synchronous in this example. For simplification, single spikes may have the following form:

Each discrete impulse-wave expands with 1 meter per second. In case of a circular expansion, the pulses reach the 30 different electrodes (0...29) at different times, if they come from different locations on the field. We suggest a homogenous (discrete) wave-space with delays proportional to the distance between the spiking neuron and the electrode.

If each "neuron" pulses once, we get following time-functions at thirty electrodes (channel origins 0...29):

(The time-functions seem to look like EEG-samples or acoustic data streams).

Reconstruction: Channel to Generator Space

Using PSI-Tools, we calculate the interference integrals for each generator-pixel (neuron) from the above channel data stream. The result is the following part of an *.avi-movie.

Click here to start a higher resolution movie (141kB)

We find the generating neuron's fire in the same moment. The reconstruction appears not perfect, the reconstruction quality appears proportional to a lot of parameters, like channel number, velocity, space distances, channel arrangements and delays.

To examine the reconstruction parameters, click here to inspect the ini-file used by PSI-Tools.


Next example for a Reconstruction

This 30-channel time-function illustrates waves which interfere to the GFaI-symbol

Click here to start the movie (680kB)

For advertising purposes it is possible, to generate data streams also with other logos in a higher quality. It looks nice, to use a water bassin to interfere such waves. The channel data stream would be the same as used for PSI-Tools. We find the neurones fired synchronous (parallel).


Reconstructive Pseudo-Wave Field

Time inversion. Reconstruction (negated time) for four channels. This is the standard way, PSI-Tools produces interference images in reconstructive form. Pulsing neurons fired one by one onto four channels. These are the locations, where four waves meet. We find impanding waves of the so called pseudo-wave field. (It has no similarities with the original, generating wave field - only the approximatly equivalent interference integrals). Surprising, that the wave front is really inside the waves!

Click here to start a *.AVI (247kB)


Projective Wave Field

The movie looks like a original wave field or a projection. Pulse waves come from channel source points, meeting at interference locations. But attention: Really it is produced with "trick 17" with time inverted time function of pulses(!) as a reconstruction onto a detector field with reverse play of the movie(!) - trick for the calculation of a detecting wave field of a projection. (Think about, draw an image - it is the same thing!)

Click here to get the zipped movie (860kB/13MB)


Reconstruction of Serial Fire

For additive superimposition the amplitude at the excitment position will be n-times higher the amplitude of the single wave, where n is the channel number. The example should give an interesting, new view on the 'integrate and fire' principle in terms of spatial arrangements. Neurons are placed again in form of the character 'G'. They fire at different times with a delay of approximately 0.5 ms. In the reconstruction we find the interferences really coming from single points.

Click here to get the *.AVI

The excitement scale is the same over the images of the movie, we used 16 channels here.


Cross interference versus small Channel Number

Known from optics, over-conditioning problems of higher channel numbers restrict the image quality of projections. But using small numbers of channels, the possibility for phantom-excitement (cross-interference within the image) grows! So the nature of our nervous system has to solve a dramatic conflict - find the best channel number for each signal connection between locations.

To remove cross interference we only can increase the delay between pulses. We include a pause between following pulses, while the channel remains still. The delay has to be greater the delay an impulse needs, to cross the detector field (field diagonale divided through speed), the resulting image appears perfect. We generate a four channel time function, the "electrodes" are at the corners.

Interference-integral of the 4-channel data set in 3D-view (PSI-Tools). Integration (over time axis) is necessarry, to get elementary wave-interferences appearing at different times into one excitment map.


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file created sept. 30, 1995

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