  We provide a simple analysis of the Douglas-Rachford splitting algorithm in
the context of $\ell^1$ minimization with linear constraints, and quantify the
asymptotic linear convergence rate in terms of principal angles between
relevant vector spaces. In the compressed sensing setting, we show how to bound
this rate in terms of the restricted isometry constant. More general iterative
schemes obtained by $\ell^2$-regularization and over-relaxation including the
dual split Bregman method are also treated, which answers the question how to
choose the relaxation and soft-thresholding parameters to accelerate the
asymptotic convergence rate. We make no attempt at characterizing the transient
regime preceding the onset of linear convergence.
