 Basis pursuit denoising

In applied mathematics and statistics, basis pursuit denoising (BPDN) refers to a mathematical optimization problem of the form

where formula_2 is a parameter that controls the trade-off between sparsity and reconstruction fidelity, formula_3 is an formula_4 solution vector, formula_5 is an formula_6 vector of observations, formula_7 is an formula_8 transform matrix and formula_9.This is an instance of convex optimization and also of quadratic programming.