 Either types of basis pursuit denoising solve a regularization problem with a trade-off between having a small residual (making formula_5 close to formula_14 in terms of the squared error) and making formula_3 simple in the formula_16-norm sense.It can be thought of as a mathematical statement of Occam's razor, finding the simplest possible explanation (i.e.one that yields formula_17) capable of accounting for the observations formula_5.