  The convergence rate is analyzed for the SpaSRA algorithm (Sparse
Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) +
\psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth.
It is shown that if $f$ is convex, then the error in the objective function at
iteration $k$, for $k$ sufficiently large, is bounded by $a/(b+k)$ for suitable
choices of $a$ and $b$. Moreover, if the objective function is strongly convex,
then the convergence is $R$-linear. An improved version of the algorithm based
on a cycle version of the BB iteration and an adaptive line search is given.
The performance of the algorithm is investigated using applications in the
areas of signal processing and image reconstruction.
