Information theoretic bounds for compressed sensing in SAR imaging

35th International Symposium on Remote Sensing of Environment

地球科学;生态环境科学

Zhang, Jingxiong^1 ; Yang, Ke^1 ; Guo, Jianzhong^2

School of Remote Sensing and Information Engineering, Wuhan University, Wuhan, China^1

School of Electronic and Electrical Engineering, Wuhan Textile University, Wuhan, China^2

关键词: Detection error probability;    Information channels;    Information theoretic bounds;    Lower and upper bounds;    Rate distortion characteristics;    Shannon Sampling Theorem;    Signals of interests;    Sub-Nyquist sampling;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/17/1/012273/pdf
DOI  :  10.1088/1755-1315/17/1/012273

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

Compressed sensing (CS) is a new framework for sampling and reconstructing sparse signals from measurements significantly fewer than those prescribed by Nyquist rate in the Shannon sampling theorem. This new strategy, applied in various application areas including synthetic aperture radar (SAR), relies on two principles: sparsity, which is related to the signals of interest, and incoherence, which refers to the sensing modality. An important question in CS-based SAR system design concerns sampling rate necessary and sufficient for exact or approximate recovery of sparse signals. In the literature, bounds of measurements (or sampling rate) in CS have been proposed from the perspective of information theory. However, these information-theoretic bounds need to be reviewed and, if necessary, validated for CS-based SAR imaging, as there are various assumptions made in the derivations of lower and upper bounds on sub-Nyquist sampling rates, which may not hold true in CS-based SAR imaging. In this paper, information-theoretic bounds of sampling rate will be analyzed. For this, the SAR measurement system is modeled as an information channel, with channel capacity and rate-distortion characteristics evaluated to enable the determination of sampling rates required for recovery of sparse scenes. Experiments based on simulated data will be undertaken to test the theoretic bounds against empirical results about sampling rates required to achieve certain detection error probabilities.