Informational analysis for compressive sampling in radar imaging.

Jingxiong Zhang,Ke Yang

doi:10.3390/s150407136

Abstract

Compressive sampling or compressed sensing (CS) works on the assumption of the sparsity or compressibility of the underlying signal, relies on the trans-informational capability of the measurement matrix employed and the resultant measurements, operates with optimization-based algorithms for signal reconstruction and is thus able to complete data compression, while acquiring data, leading to sub-Nyquist sampling strategies that promote efficiency in data acquisition, while ensuring certain accuracy criteria. Information theory provides a framework complementary to classic CS theory for analyzing information mechanisms and for determining the necessary number of measurements in a CS environment, such as CS-radar, a radar sensor conceptualized or designed with CS principles and techniques. Despite increasing awareness of information-theoretic perspectives on CS-radar, reported research has been rare. This paper seeks to bridge the gap in the interdisciplinary area of CS, radar and information theory by analyzing information flows in CS-radar from sparse scenes to measurements and determining sub-Nyquist sampling rates necessary for scene reconstruction within certain distortion thresholds, given differing scene sparsity and average per-sample signal-to-noise ratios (SNRs). Simulated studies were performed to complement and validate the information-theoretic analysis. The combined strategy proposed in this paper is valuable for information-theoretic orientated CS-radar system analysis and performance evaluation.

Highlights

Compressed sensing (CS) is a new methodology for information acquisition and processing, as it provides a framework for directly acquiring data already in compressed form, promoting under-sampling or sub-Nyquist sampling strategies that are more efficient than what is required by the Shannon–Nyquist sampling theorem [2,3]
To implement CS with radar imaging, we can use real representations for the complex-valued radar images [48], so that the CS techniques designed for real-valued signals can be employed, given that analysis and algorithms for complex signals are not well developed
This paper provided the informational description, analysis and interpretation of information flows from the source, through the measurements, to the destination

Summary

Introduction

Compressed sensing (CS) is a new methodology for information acquisition and processing, as it provides a framework for directly acquiring data already in compressed form (rather than the conventional sampling-compression practice [1]), promoting under-sampling or sub-Nyquist sampling strategies that are more efficient than what is required by the Shannon–Nyquist sampling theorem [2,3]. CS works on the assumption of the sparsity of the scene being sensed, relies on the informational transferability of the sensing/measurement matrices in capturing the information content in the underlying signal (or scene in the context of radar) and operates through algorithms that can reconstruct the sparse signal from under-sampled data [7,12,13,14,15,16]. We can examine signal sparsity or compressibility (so, there has been much work on image compression [1,21] before the advent of CS), measurement matrices, signal reconstruction and other elements in a CS context based on informational analysis [22,23,24]. Fano inequality, rate distortion and the channel coding theorem are often applied for undersampling theorem developments [26,27,28], while statistical analysis of the signal reconstruction process (e.g., error probability bounds in signal reconstruction, especially when used in connection with Fano inequality) is an important ingredient [29]

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