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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.
This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$-ary hypothesis testing in terms of the Arimoto-Renyi conditional entropy of an arbitrary order $alpha$. The improved tightness of these bounds over their specializ
We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and exponents of th
We consider the problem of distributed binary hypothesis testing of two sequences that are generated by an i.i.d. doubly-binary symmetric source. Each sequence is observed by a different terminal. The two hypotheses correspond to different levels of
We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from the distri
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis is importan