What's the difference between a dictionary and a basis?

[PhillipKP]

I see the term dictionary used a lot and it sounds a lot like a basis for a vector space. But what is the different? Can we collection of vectors be both a basis and a dictionary?

Thanks

 

[micromass]

Hi PhillipKP!

Can you give me some kind of reference where the word "dictionary" is used? I have never seen it being used before.

 

[PhillipKP]

It's used in signal processing and specifically in the new field of compressive sensing.

This is where I first encountered it: http://www-stat.stanford.edu/~candes/papers/CoherentCS.pdf

 

[micromass]

A dictionary seems to be a tool to translate n-dimensional systems into k-dimensional systems. I don't really see a connection to a basis here. It's just matrix that gives a transformation of signals...

Then again, I know nothing of signal processing...

 

[PhillipKP]

No worries. :)