  There have been many matching pursuit algorithms (MPAs) which handle the
sparse signal recovery problem a.k.a. compressed sensing (CS). In the MPAs, the
correlation computation step has a dominant computational complexity. In this
letter, we propose a new fast correlation computation method when we use some
classes of partial unitary matrices as the sensing matrix. Those partial
unitary matrices include partial Fourier matrices and partial Hadamard matrices
which are popular sensing matrices. The proposed correlation computation method
can be applied to almost all MPAs without causing any degradation of their
recovery performance. And, for most practical parameters, the proposed method
can reduce the computational complexity of the MPAs substantially.
