{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:30:22Z","timestamp":1740137422948,"version":"3.37.3"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"the EU FP7 Project LIVCODE","award":["295151"],"award-info":[{"award-number":["295151"]}]},{"name":"the Science Research Project of Ningxia Higher Education Institutions of China","award":["NGY20140147"],"award-info":[{"award-number":["NGY20140147"]}]},{"name":"the Science Research Project of the State Ethnic Affairs Commission of China","award":["14BFZ002"],"award-info":[{"award-number":["14BFZ002"]}]},{"name":"the Science Research Project of Beifang University of Nationalities","award":["2015JBK421","2016SXKY07"],"award-info":[{"award-number":["2015JBK421","2016SXKY07"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China (NSFC)","doi-asserted-by":"crossref","award":["61261043"],"award-info":[{"award-number":["61261043"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p> In practical examples, there are numerous signals that are sparse in a redundant frame rather than an orthonormal basis. This paper mainly focuses on such sparse recovery via [Formula: see text]-analysis-based dual frame with Weibull matrices under the assumption that signals are sparse or compressible in a general frame. First, we give the [Formula: see text] robust null space property and show that it is weaker than the [Formula: see text]-RIP when [Formula: see text] is a general frame. Second, we show that Weibull random matrices with a general dual frame satisfy the [Formula: see text] robust null space property with high probability. Finally, we investigate the stability estimate of [Formula: see text]-analysis based dual frame with Weibull matrices. The result shows that it remains stable and can guarantee accurate recovery of signals with high probability. <\/jats:p>","DOI":"10.1142\/s0219691317500011","type":"journal-article","created":{"date-parts":[[2016,10,19]],"date-time":"2016-10-19T06:24:36Z","timestamp":1476858276000},"page":"1750001","source":"Crossref","is-referenced-by-count":3,"title":["Stability of lq-analysis based dual frame with Weibull matrices for 0 &lt; q \u2264 1"],"prefix":"10.1142","volume":"15","author":[{"given":"Yi","family":"Gao","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, Ningxia 750021, P. R. China"}]},{"given":"Shigang","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Computer Science, University of Lincoln, Lincoln LN6 7TS, UK"}]},{"given":"Yongdong","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, Ningxia 750021, P. R. 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