Basis pursuit

Basis pursuit is the mathematical optimization problem of the form:

where x is a N × 1 solution vector (signal), y is a M × 1 vector of observations (measurements), A is a M × N transform matrix (usually measurement matrix) and M < N.

It is usually applied in cases where there is an underdetermined system of linear equations y = Ax that must be exactly satisfied, and the sparsest solution in the L1 sense is desired.

When it is desirable to trade off exact equality of Ax and y in exchange for a sparser x, basis pursuit denoising is preferred.

See also

References & further reading

  • Stephen Boyd, Lieven Vandenbergh: Convex Optimization, Cambridge University Press, 2004, ISBN 9780521833783, pp. 337-337
  • Simon Foucart, Holger Rauhut: A Mathematical Introduction to Compressive Sensing. Springer, 2013, ISBN 9780817649487, pp. 77-110


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