Parallelizing Basis Pursuit Denoising

Basis Pursuit DeNoising (BPDN) is a version of sparse least squares, where there is an ℓ
¹
penalty for the coefficients in addition to the sum of squares of the errors. To apply this technique to large data sets, parallel algorithms are needed. In this paper, we create a parallel version of a BPDN algorithm [11] that can compute exact solutions for an interval of values for the ℓ
¹
penalty parameter that exploits the sparsity of the solutions, unlike stochastic gradient descent-type algorithms.