【摘要】：壓縮感知(compressed sensing or compressive sampling,CS)是數(shù)據(jù)采集與信號重構的新體制,其與信息論的關系是,應該且可以從信息論的角度對CS進行分析,而CS豐富和發(fā)展著信息論的內(nèi)涵和外延。換言之,信息論的一些基本概念和原理(如信源、信道、信源編碼、信道編碼、率失真、Fano不等式、數(shù)據(jù)處理定理等)為CS研究提供了理論基礎,尤其是在性能限(如采樣數(shù))的界定等方面;另一方面,CS提供了采集、存貯、傳輸、恢復稀疏信號的高效方法,以其獨特的理念和算法模式,提供了直接對信息的采樣和處理機制,延拓了經(jīng)典信息論的范疇。本文將梳理和闡釋CS和信息論之間的關系,力圖從信息論角度揭示CS中的一些基本問題,尤其是CS采樣問題,并尋求用信息論指導CS的學習與研究。
[Abstract]:Compressed perceptual (compressed sensing or compressive sampling,CS (compressed sensing or compressive sampling,CS) is a new system of data acquisition and signal reconstruction. Its relationship with information theory is that CS should and can be analyzed from the angle of information theory, and CS enriches and develops the connotation and extension of information theory. In other words, some basic concepts and principles of information theory (such as source, channel, source coding, channel coding, rate-distortion Fano inequality, data processing theorem, etc.) provide a theoretical basis for the study of CS. On the other hand, CS provides an efficient method of collecting, storing, transmitting and restoring sparse signal, with its unique idea and algorithm mode. The mechanism of direct sampling and processing of information is provided, and the category of classical information theory is extended. This paper will comb and explain the relationship between CS and information theory, try to reveal some basic problems in CS from the angle of information theory, especially the problem of CS sampling, and seek to use information theory to guide the study and research of CS.
【作者單位】： 武漢大學遙感信息工程學院;武漢紡織大學電子與電氣工程學院;
【基金】：國家973計劃資助項目(2010CB731905) 國家自然科學基金資助項目(41071286) 湖北省教育廳基金資助項目(D201416022)~~
【分類號】：TN911.7
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本文編號：2256268