  Orthogonal least square (OLS) is an important sparse signal recovery
algorithm for compressive sensing, which enjoys superior probability of success
over other well-known recovery algorithms under conditions of correlated
measurement matrices. Multiple OLS (mOLS) is a recently proposed improved
version of OLS which selects multiple candidates per iteration by generalizing
the greedy selection principle used in OLS and enjoys faster convergence than
OLS. In this paper, we present a refined version of the mOLS algorithm where at
each step of the iteration, we first preselect a submatrix of the measurement
matrix suitably and then apply the mOLS computations to the chosen submatrix.
Since mOLS now works only on a submatrix and not on the overall matrix,
computations reduce drastically. Convergence of the algorithm, however,
requires ensuring passage of true candidates through the two stages of
preselection and mOLS based selection successively. This paper presents
convergence conditions for both noisy and noise free signal models. The
proposed algorithm enjoys faster convergence properties similar to mOLS, at a
much reduced computational complexity.
