Constructing test instances for Basis Pursuit Denoising
  The number of available algorithms for the so-called Basis Pursuit Denoising problem (or the related LASSO-problem) is large and keeps growing. Similarly, the number of experiments to evaluate and compare these algorithms on different instances is growing.   In this note, we present a method to produce instances with exact solutions which is based on a simple observation which is related to the so called source condition from sparse regularization. 
Dirk A. Lorenz
cs.IT math.IT