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Keywords
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Compressive sensing, cumulative extropy, maximum ranked set sampling, record ranked set sampling, stochastic ordering.
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Abstract
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The aim of this paper is to consider the extropy measure of uncertainty proposed by Lad,
Sanfilippo and Agro for the problem of compressive sensing. For this purpose, two sampling designs,
i.e., simple random sampling (SRS) and a modified version of ranked set sampling, known as maximum
ranked set sampling procedure with unequal samples (MRSSU), are utilized and some uncertainty
measures such as extropy, cumulative extropy and residual extropy are obtained and compared for
these sampling designs. Also, some results of extropy in record ranked set sampling data are developed.
Then a study on comparing the behavior of estimators of cumulative extropy in MRSSU and SRS
using simulation method is obtained. As an example, two sampling methods MRSSU and SRS are
utilized for compressive sensing technique and their performances are compared via signal to noise ratio
(SNR), correlation coefficient of reconstructed and the original signal and cumulative extropy measure
of uncertainty. The results show that the values of SNR and correlation coefficient for MRSSU are
higher than those of SRS. Furthermore, it is shown that MRSSU scheme can efficiently reduce the
uncertainty measure of cumulative extropy.
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