Abstract
Assuming sparsity or compressibility of the underlying signals, compressed sensing or compressive sampling (CS) exploits the informational efficiency of under-sampled measurements for increased efficiency yet acceptable accuracy in information gathering, transmission and processing, though it often incurs extra computational cost in signal reconstruction. Shannon information quantities and theorems, such as source rate-distortion, trans-information and rate distortion theorem concerning lossy data compression, provide a coherent framework, which is complementary to classic CS theory, for analyzing informational quantities and for determining the necessary number of measurements in CS. While there exists some information-theoretic research in the past on CS in general and compressive radar imaging in particular, systematic research is needed to handle issues related to scene description in cluttered environments and trans-information quantification in complex sparsity-clutter-sampling-noise settings. The novelty of this paper lies in furnishing a general strategy for information-theoretic analysis of scene compressibility, trans-information of radar echo data about the scene and the targets of interest, respectively, and limits to undersampling ratios necessary for scene reconstruction subject to distortion given sparsity-clutter-noise constraints. A computational experiment was performed to demonstrate informational analysis regarding the scene-sampling-reconstruction process and to generate phase transition diagrams showing relations between undersampling ratios and sparsity-clutter-noise-distortion constraints. The strategy proposed in this paper is valuable for information-theoretic analysis and undersampling theorem developments in compressive radar imaging and other computational imaging applications.
Highlights
Unlike the traditional practice of sampling followed by compression, compressive sampling (CS) provides a framework for directly acquiring data in compressed form, promoting sub-Nyqusit sampling that is more efficient than what is required by the Shannon-Nyquist sampling theorem [1,2,3]
In this sub-section, we discuss the results by first comparing undersampling ratios derived from information-theoretic analysis and those based on the restricted isometry property (RIP) in classical CS
This paper has presented an information-theoretic strategy, which is seen to be complementary to the classic CS theory, to describe, analyze and interpret information dynamics in compressive radar imaging
Summary
Unlike the traditional practice of sampling followed by compression, CS provides a framework for directly acquiring data in compressed form, promoting sub-Nyqusit sampling that is more efficient than what is required by the Shannon-Nyquist sampling theorem [1,2,3]. The studies concern: (1) informationtheoretic characterization of compressibility of radar scenes, (2) trans-information quantification of radar measurements about the underlying scene and about the targets of interest against a cluttered background, respectively, and (3) derivation of necessary sampling ratios for signal reconstruction at a range of distortion tolerances. (2) A generalized approach is proposed for quantifying trans-information between noisy measurements and the underlying scene as a whole and between the measurements and targets of interest against clutter interference, in particular, with the latter providing a more contingent benchmark for sparse target detection and estimation; this is accomplished through derivation of undersampled data’s joint differential entropy and trans-information in the context of deterministic measurement matrices, which are common in remote sensing applications;.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
