{"title":"压缩感知的近最优压缩","authors":"Rayan Saab, Rongrong Wang, Ö. Yilmaz","doi":"10.1109/DCC.2015.31","DOIUrl":null,"url":null,"abstract":"In this note we study the under-addressed quantization stage implicit in any compressed sensing signal acquisition paradigm. We also study the problem of compressing the bitstream resulting from the quantization. We propose using Sigma-Delta (ΣΔ) quantization followed by a compression stage comprised of a discrete Johnson-Lindenstrauss embedding, and a subsequent reconstruction scheme based on convex optimization. We show that this encoding/decoding method yields near-optimal rate-distortion guarantees for sparse and compressible signals and is robust to noise. Our results hold for sub-Gaussian (including Gaussian and Bernoulli) random compressed sensing measurements, and they hold for high bit-depth quantizers as well as for coarse quantizers including 1-bit quantization.","PeriodicalId":313156,"journal":{"name":"2015 Data Compression Conference","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Near-Optimal Compression for Compressed Sensing\",\"authors\":\"Rayan Saab, Rongrong Wang, Ö. Yilmaz\",\"doi\":\"10.1109/DCC.2015.31\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note we study the under-addressed quantization stage implicit in any compressed sensing signal acquisition paradigm. We also study the problem of compressing the bitstream resulting from the quantization. We propose using Sigma-Delta (ΣΔ) quantization followed by a compression stage comprised of a discrete Johnson-Lindenstrauss embedding, and a subsequent reconstruction scheme based on convex optimization. We show that this encoding/decoding method yields near-optimal rate-distortion guarantees for sparse and compressible signals and is robust to noise. Our results hold for sub-Gaussian (including Gaussian and Bernoulli) random compressed sensing measurements, and they hold for high bit-depth quantizers as well as for coarse quantizers including 1-bit quantization.\",\"PeriodicalId\":313156,\"journal\":{\"name\":\"2015 Data Compression Conference\",\"volume\":\"16 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-04-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 Data Compression Conference\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/DCC.2015.31\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 Data Compression Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DCC.2015.31","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this note we study the under-addressed quantization stage implicit in any compressed sensing signal acquisition paradigm. We also study the problem of compressing the bitstream resulting from the quantization. We propose using Sigma-Delta (ΣΔ) quantization followed by a compression stage comprised of a discrete Johnson-Lindenstrauss embedding, and a subsequent reconstruction scheme based on convex optimization. We show that this encoding/decoding method yields near-optimal rate-distortion guarantees for sparse and compressible signals and is robust to noise. Our results hold for sub-Gaussian (including Gaussian and Bernoulli) random compressed sensing measurements, and they hold for high bit-depth quantizers as well as for coarse quantizers including 1-bit quantization.