{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:25:32Z","timestamp":1740147932596,"version":"3.37.3"},"reference-count":16,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171018","2010CB732501"],"award-info":[{"award-number":["11171018","2010CB732501"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Basic Research Program of China","doi-asserted-by":"crossref","award":["11171018","2010CB732501"],"award-info":[{"award-number":["11171018","2010CB732501"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2012]]},"abstract":"Compressive sensing microarrays (CSM) are DNA-based sensors that operate using group testing and compressive sensing principles. Mathematically, one can cast the CSM as sparse nonnegative recovery (SNR) which is to find the sparsest solutions subjected to an underdetermined system of linear equations and nonnegative restriction. In this paper, we discuss thel<\/mml:mi>1<\/mml:mn><\/mml:msub><\/mml:mrow><\/mml:math>relaxation of the SNR. By defining nonnegative restricted isometry\/orthogonality constants, we give a nonnegative restricted property condition which guarantees that the SNR and thel<\/mml:mi>1<\/mml:mn><\/mml:msub><\/mml:mrow><\/mml:math>relaxation share the common unique solution. 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