{"title":"基于噪声测量的非凸压缩感知","authors":"A. Majumdar, R. Ward","doi":"10.2174/1876825300902010040","DOIUrl":null,"url":null,"abstract":"This paper proposes solution to the following non-convex optimization problem: min || x || p subject to || yAx || q Such an optimization problem arises in a rapidly advancing branch of signal processing called 'Compressed Sensing' (CS). The problem of CS is to reconstruct a k-sparse vector xnX1, from noisy measurements y = Ax+, where AmXn (m<n) is the measurement matrix andmX1 is additive noise. In general the optimization methods developed for CS minimizes a sparsity promoting l1-norm (p=1) for Gaussian noise (q=2). This is restrictive for two reasons: i) theoretically it has been shown that, with positive fractional norms (0<p<1), the sparse vector x can be reconstructed by fewer measurements than required by l1-norm; and ii) Noises other than Gaus- sian require the norm of the misfit (q) to be something other than 2. To address these two issues an Iterative Reweighted Least Squares based algorithm is proposed here to solve the aforesaid optimization problem.","PeriodicalId":147157,"journal":{"name":"The Open Signal Processing Journal","volume":"181 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Non-Convex Compressed Sensing from Noisy Measurements\",\"authors\":\"A. Majumdar, R. Ward\",\"doi\":\"10.2174/1876825300902010040\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper proposes solution to the following non-convex optimization problem: min || x || p subject to || yAx || q Such an optimization problem arises in a rapidly advancing branch of signal processing called 'Compressed Sensing' (CS). The problem of CS is to reconstruct a k-sparse vector xnX1, from noisy measurements y = Ax+, where AmXn (m<n) is the measurement matrix andmX1 is additive noise. In general the optimization methods developed for CS minimizes a sparsity promoting l1-norm (p=1) for Gaussian noise (q=2). This is restrictive for two reasons: i) theoretically it has been shown that, with positive fractional norms (0<p<1), the sparse vector x can be reconstructed by fewer measurements than required by l1-norm; and ii) Noises other than Gaus- sian require the norm of the misfit (q) to be something other than 2. To address these two issues an Iterative Reweighted Least Squares based algorithm is proposed here to solve the aforesaid optimization problem.\",\"PeriodicalId\":147157,\"journal\":{\"name\":\"The Open Signal Processing Journal\",\"volume\":\"181 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-12-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Open Signal Processing Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2174/1876825300902010040\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Open Signal Processing Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2174/1876825300902010040","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Non-Convex Compressed Sensing from Noisy Measurements
This paper proposes solution to the following non-convex optimization problem: min || x || p subject to || yAx || q Such an optimization problem arises in a rapidly advancing branch of signal processing called 'Compressed Sensing' (CS). The problem of CS is to reconstruct a k-sparse vector xnX1, from noisy measurements y = Ax+, where AmXn (m
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