  A greedy algorithm called Bayesian multiple matching pursuit (BMMP) is
proposed to estimate a sparse signal vector and its support given $m$ linear
measurements. Unlike the maximum a posteriori (MAP) support detection, which
was proposed by Lee to estimate the support by selecting an index with the
maximum likelihood ratio of the correlation given by a normalized version of
the orthogonal matching pursuit (OMP), the proposed method uses the correlation
given by the matching pursuit proposed by Davies and Eldar. BMMP exploits the
diversity gain to estimate the support by considering multiple support
candidates, each of which is obtained by iteratively selecting an index set
with a size different for each candidate. In particular, BMMP considers an
extended support estimate whose maximal size is $m$ in the process to obtain
each of the support candidates. It is observed that BMMP outperforms other
state-of-the-art methods and approaches the ideal limit of the signal sparsity
in our simulation setting.
