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Signal Process."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we present a non-convex <jats:italic>\u2113<\/jats:italic><jats:sub>2<\/jats:sub>\/<jats:italic>\u2113<\/jats:italic><jats:sub><jats:italic>q<\/jats:italic><\/jats:sub>(0&lt;<jats:italic>q<\/jats:italic>&lt;1)-analysis method to recover a general signal that can be expressed as a block-sparse coefficient vector in a coherent tight frame, and a sufficient condition is simultaneously established to guarantee the validity of the proposed method. In addition, we also derive an efficient iterative re-weighted least square (IRLS) algorithm to solve the induced non-convex optimization problem. The proposed IRLS algorithm is tested and compared with the <jats:italic>\u2113<\/jats:italic><jats:sub>2<\/jats:sub>\/<jats:italic>\u2113<\/jats:italic><jats:sub>1<\/jats:sub>-analysis and the <jats:italic>\u2113<\/jats:italic><jats:sub><jats:italic>q<\/jats:italic><\/jats:sub>(0&lt;<jats:italic>q<\/jats:italic>\u22641)-analysis methods in some experiments. All the comparisons demonstrate the superior performance of the <jats:italic>\u2113<\/jats:italic><jats:sub>2<\/jats:sub>\/<jats:italic>\u2113<\/jats:italic><jats:sub><jats:italic>q<\/jats:italic><\/jats:sub>-analysis method with 0&lt;<jats:italic>q<\/jats:italic>&lt;1.<\/jats:p>","DOI":"10.1186\/s13634-019-0659-8","type":"journal-article","created":{"date-parts":[[2020,1,23]],"date-time":"2020-01-23T13:02:54Z","timestamp":1579784574000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Non-convex block-sparse compressed sensing with coherent tight frames"],"prefix":"10.1186","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1897-6832","authenticated-orcid":false,"given":"Xiaohu","family":"Luo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanzhen","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jincai","family":"Ha","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xing","family":"Ai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xishan","family":"Tian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,1,23]]},"reference":[{"key":"659_CR1","series-title":"Undergraduate Topics in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84800-072-8","volume-title":"A Concise Introduction to Data Compression","author":"David Salomon","year":"2008","unstructured":"D. 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