RMP: Reduced-set matching pursuit approach for efficient compressed sensing signal reconstruction

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• 作者：Michael M. Abdel-Sayed ; Ahmed Khattab<sup> ; sup><sup>akhattab@ieee.org" class="auth_mail" title="E-mail the corresponding authorsup> ; Mohamed F. Abu-Elyazeed
• 关键词：Compressed sensing ; Matching pursuit ; Sparse signal reconstruction ; Restricted isometry property
• 刊名：Journal of Advanced Research
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：7
• 期：6
• 页码：851-861
• 全文大小：1176 K

文摘

Compressed sensing enables the acquisition of sparse signals at a rate that is much lower than the Nyquist rate. Compressed sensing initially adopted <span id="mmlsi5" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S2090123216300583&_mathId=si5.gif&_user=111111111&_pii=S2090123216300583&_rdoc=1&_issn=20901232&md5=de98e6aa71f702ffeeacde1208971a74" title="Click to view the MathML source">ℓ<sub>1sub>span><span class="mathContainer hidden"><span class="mathCode">scroll">sub>ℓ1sub>span>span>span> minimization for signal reconstruction which is computationally expensive. Several greedy recovery algorithms have been recently proposed for signal reconstruction at a lower computational complexity compared to the optimal <span id="mmlsi5" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S2090123216300583&_mathId=si5.gif&_user=111111111&_pii=S2090123216300583&_rdoc=1&_issn=20901232&md5=de98e6aa71f702ffeeacde1208971a74" title="Click to view the MathML source">ℓ<sub>1sub>span><span class="mathContainer hidden"><span class="mathCode">scroll">sub>ℓ1sub>span>span>span> minimization, while maintaining a good reconstruction accuracy. In this paper, the Reduced-set Matching Pursuit (RMP) greedy recovery algorithm is proposed for compressed sensing. Unlike existing approaches which either select too many or too few values per iteration, RMP aims at selecting the most sufficient number of correlation values per iteration, which improves both the reconstruction time and error. Furthermore, RMP prunes the estimated signal, and hence, excludes the incorrectly selected values. The RMP algorithm achieves a higher reconstruction accuracy at a significantly   low computational complexity compared to existing greedy recovery algorithms. It is even superior to <span id="mmlsi5" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S2090123216300583&_mathId=si5.gif&_user=111111111&_pii=S2090123216300583&_rdoc=1&_issn=20901232&md5=de98e6aa71f702ffeeacde1208971a74" title="Click to view the MathML source">ℓ<sub>1sub>span><span class="mathContainer hidden"><span class="mathCode">scroll">sub>ℓ1sub>span>span>span> minimization in terms of the normalized time-error product, a new metric introduced to measure the trade-off between the reconstruction time and error. RMP superior performance is illustrated with both noiseless and noisy samples.