Compressive Sensing Theory (Maths)

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... is pretty damn impressive.

While I lack about a lifetime in maths to properly follow the stuff, basically it states that a near perfect reconstruction of complex signals is possible from extremely sparse starting data.

Or in other words, that "simplest solution is the best" is surprisingly true.

If I get this right, the algorithms used (l1 - minimization based) when, for example, trying to fill in missing pixels test the shapes on the picture. Each complex shape is made out of simpler ones. The algorithms decide which would be the simplest shape gained if another pixel was added, add it, and repeat this over and over until the picture is reconstructed, always choosing the simplest route. I could be getting it all completely wrong.

Basically, sparse well chosen data is just as good as rich data. There is nothing to fear in inherent uncertainty.

The approach has lead to single pixel camera.


... and there is something fascinating about imagining a future in which photographs are not trying to record reality as accurately as they can, but sampling bits of it, which alone, mean nothing, and trusting mathematics to show reality anyway.

A world embracing its quantum origins.


In case anyone is interested:

For non-mathematicians

MATLAB routines, examples

Math stuff .pdf file (Overview of some l1 minimizaton algorithms, math article)


P.S. Would make an awesome Sci-Fi story premise:
What if you took photographs with the CS approach, but got a completely different reality out of it?
What if your own reality stops following the simplicity principle but the photos still do?

P.S.2:
I'm in RP withdrawal, in case you can't tell.

 

Have you ever had a dream where you’re having a discussion with someone and, while you think you are conversing quite intelligently, at some point during the conversation you realize that you haven’t got a freakin' clue about what the other person is talking about?

That’s what this topic reminds me of…

 

... I thought it was going to be conversation about being on bottom.

 

That's all Greek to me but this I find interesting:

It reminded me of the Non-Euclidian extradimensional beings of the Cthulhu mythos.

I'm pretty sure that you have a really cool basis for a cosmic horror story.

 

Heh. Sorry.

Most my e-mail discussions hit that stage at one point or another. Both sides struggling vigorously to explain their points to the opposition and both sort-of-talking about completely unrelated issues.

But, um... yes. As evidence indicates, clarity never was my strong side.

On the plus side, the fact that you'd get no absolute certainty out of a CS reconstructed photograph could provide an alternate explanation of some alpacas... that would call for the summoning of Statistical Beast of the "H"s ... and then we'd really be in trouble.

Cara:
That would be pretty snazzy.
I would settle for a exploration of the delineation of reality of the place - through constant comparison of photo-world and real world, given my non-existent skills at horror. Would be a great place to play with physics.

 

The comparison between photo world and real world makes me thing about Blowup; a 1966 thriller about a photographer who believes that he has taken the picture of a murder. I like your idea, you should definitely give it a try.