  In this paper, we propose a Bayesian Hypothesis Testing Algorithm (BHTA) for
sparse representation. It uses the Bayesian framework to determine active atoms
in sparse representation of a signal.
  The Bayesian hypothesis testing based on three assumptions, determines the
active atoms from the correlations and leads to the activity measure as
proposed in Iterative Detection Estimation (IDE) algorithm. In fact, IDE uses
an arbitrary decreasing sequence of thresholds while the proposed algorithm is
based on a sequence which derived from hypothesis testing. So, Bayesian
hypothesis testing framework leads to an improved version of the IDE algorithm.
  The simulations show that Hard-version of our suggested algorithm achieves
one of the best results in terms of estimation accuracy among the algorithms
which have been implemented in our simulations, while it has the greatest
complexity in terms of simulation time.
