You may refer to:

http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms

You can find a few of them (also thanks to the interest in compressive sensing), e.g.:

http://statweb.stanford.edu/~candes/nesta/

http://kl1p.sourceforge.net/home.html

There is a rather comprehesive list of codes for CS here, a couple at least are in C++:

https://sites.google.com/site/igorcarron2/cs#reconstruction

By the way, if you are looking for basis pursuit denoising (or LASSO), most of the good machine learning libraries in C++ have their own implementation, e.g.:

http://www.mlpack.org/doxygen.php?doc=classmlpack_1_1regression_1_1LARS.html

http://www.shogun-toolbox.org/

I'd recommend using python as an alternative to Matlab instead of C++. It is as easy to use as Matlab, and many libraries provide an interface to python.

E.g. http://spams-devel.gforge.inria.fr/ provides sparse modeling in C++ but also with a python or R) binding.