{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:11:02Z","timestamp":1760238662740,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2020,8,17]],"date-time":"2020-08-17T00:00:00Z","timestamp":1597622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>By means of compressive sampling (CS), a sparse signal can be efficiently recovered from its far fewer samples than that required by the Nyquist\u2013Shannon sampling theorem. However, recovering a speech signal from its CS samples is a challenging problem, as it is not sparse enough on any existing canonical basis. To solve this problem, we propose a method which combines the approximate message passing (AMP) and Markov chain that exploits the dependence between the modified discrete cosine transform (MDCT) coefficients of a speech signal. To reconstruct the speech signal from CS samples, a turbo framework, which alternately iterates AMP and belief propagation along the Markov chain, is utilized. In addtion, a constrain is set to the turbo iteration to prevent the new method from divergence. Extensive experiments show that, compared to other traditional CS methods, the new method achieves a higher signal-to-noise ratio, and a higher perceptual evaluation of speech quality (PESQ) score. At the same time, it maintaines a better similarity of the energy distribution to the original speech spectrogram. The new method also achieves a comparable speech enhancement effect to the state-of-the-art method.<\/jats:p>","DOI":"10.3390\/s20164609","type":"journal-article","created":{"date-parts":[[2020,8,17]],"date-time":"2020-08-17T06:33:20Z","timestamp":1597646000000},"page":"4609","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Speech Compressive Sampling Using Approximate Message Passing and a Markov Chain Prior"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7626-9626","authenticated-orcid":false,"given":"Xiaoli","family":"Jia","sequence":"first","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}]},{"given":"Peilin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}]},{"given":"Sumxin","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Shanghai University of Electric Power, Shanghai 200093, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/MSP.2007.914731","article-title":"An introduction to compressive sampling","volume":"25","author":"Wakin","year":"2008","journal-title":"IEEE Signal Process. 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