This is our implementation of sparse randomized Kaczmarz algorithm  to handle multiple measurements.
This will solve the system of equations
Y=AX where Y,A, and X are all matrices.
our extension is not an optimization algorithm but simple heuristic that works well for both overdetermined and underdetermined system of equations.
If you set number of multiple measurements(L) to be one then it is just the following paper.
H. Mansour and O. Yilmaz, “A Fast Randomized Kaczmarz Algorithm
for Sparse Solutions of Consistent Linear Systems,” 2013, university of
British Columbia, Vancouver - BC, Canada, arXiv:1305.3803v1.