 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" 1 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.