Sunday, February 06, 2011

Reading the Donoho-Tanner Diagram


As I was reading the Donoho-Tanner phase transition recently, I had difficulty "moving around" the graph. Here is the graph with iso-k/N curves  ( y = (k/N) / x ) with the following conventions:
  • k stands for the sparsity of the solution
  • m for the number of measurements or the number of equations
  • N for the dimension of the underlying space or the number of unknowns.
  • k/m is the under-sampling ratio
  • m/N is the over-sampling ratio

2 comments:

M.A. Turner said...

Yeah I know what you mean, I'm trying to draw parallels to thermodynamics...do you have any suggestions on that?

Igor said...

You might want to read the paper by Donoho and Tanner to see if there is a connection.

Igor.

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