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Adv. Signal Process."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The area of one-bit compressed sensing (1-bit CS) focuses on the recovery of sparse signals from binary measurements. Over the past decade, this field has witnessed the emergence of well-developed theories. However, most of the existing literature is confined to fully random measurement matrices, like random Gaussian and random sub-Gaussian measurements. This limitation often results in high generation and storage costs. This paper aims to apply semi-tensor product-based measurements to 1-bit CS. By utilizing the semi-tensor product, this proposed method can compress high-dimensional signals using lower-dimensional measurement matrices, thereby reducing the cost of generating and storing fully random measurement matrices. We propose a regularized model for this problem that has a closed-form solution. Theoretically, we demonstrate that the solution provides an approximate estimate of the underlying signal with upper bounds on recovery error. Empirically, we conduct a series of experiments on both synthetic and real-world data to demonstrate the proposed method\u2019s ability to utilize a lower-dimensional measurement matrix for signal compression and reconstruction with enhanced flexibility, resulting in improved recovery accuracy.<\/jats:p>","DOI":"10.1186\/s13634-023-01071-6","type":"journal-article","created":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T10:02:35Z","timestamp":1699005755000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Semi-tensor product-based one-bit compressed sensing"],"prefix":"10.1186","volume":"2023","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7539-8207","authenticated-orcid":false,"given":"Jingyao","family":"Hou","sequence":"first","affiliation":[]},{"given":"Xinling","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,11,3]]},"reference":[{"issue":"2","key":"1071_CR1","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1109\/TGRS.2013.2245509","volume":"51","author":"HF Shen","year":"2014","unstructured":"H.F. 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