Conventional synthetic aperture radar (SAR) systems are limited in their ability to satisfy the increasing requirement for improved spatial resolution and wider coverage. The demand for high resolution requires high sampling rates, while coverage is limited by the pulse repetition frequency. Consequently, sampling rate reduction is of high practical value in SAR imaging. In this paper, we introduce a new algorithm, equivalent to the well-known range-Doppler method, to process SAR data using the Fourier series coefficients of the raw signals. We then demonstrate how to exploit the algorithm features to reduce sampling rate in both range and azimuth axes and process the signals at sub-Nyquist rates, by using compressive sensing (CS) tools. In particular, we demonstrate recovery of an image using only a portion of the received signal’s bandwidth and also while dropping a large percentage of the transmitted pulses. The complementary pulses may be used to capture other scenes within the same coherent processing interval. In addition, we propose exploiting the ability to reconstruct the image from narrow bands in order to dynamically adapt the transmitted waveform energy to vacant spectral bands, paving the way to cognitive SAR. The proposed recovery algorithms form a new CS-SAR imaging method that can be applied to high-resolution SAR data acquired at sub-Nyquist rates in range and azimuth. The performance of our method is assessed using simulated and real data sets. Finally, our approach is implemented in hardware using a previously suggested Xampling radar prototype.
The authors in @cite_38 and @cite_1 used CS in order to reduce the rate in both dimensions. In @cite_38 RDA and CS were combined in order to exploit RDA benefits, however, only linear interpolation was considered. To achieve accurate results, the data is normally oversampled and the kernel of the interpolator may span many samples which comes at the expense of efficiency and computational load. In @cite_1 , due to its simplicity, the authors suggest a compressive sensing algorithm based on the chirp scaling algorithm (CSA). This processing technique does not require interpolation @cite_19 . Unlike RDA, this method is based on the assumption that the transmitted signal has a chirp form and is known to be less robust to noise. Both methods apply random sampling in time without proposing a practical sampling mechanism which enables the extraction of the low-rate samples directly from the analog signals.
@cite_19 @cite_38 @cite_1
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A novel compressive sensing (CS) algorithm for synthetic aperture radar (SAR) imaging is proposed which is called as the two-dimensional double CS algorithm (2-D-DCSA). We first derive the imaging operator for SAR, which is named as the chirp-scaling operator (CSO), from the chirp-scaling algorithm (CSA), then we show its inverse is a linear map, which transforms the SAR image to the received baseband radar signal. We show that the SAR image can be reconstructed simultaneously in the range and azimuth directions from a small number of the raw data. The proposed algorithm can handle large-scale data because both the CSO and its inverse allow fast matrix-vector multiplications. Both the simulated and real data are processed to test the algorithm and the results show that the 2-D-DCSA can be applied to reconstructing the SAR images effectively with much less data than regularly required. The Compressive Sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each measurement to a finite number of bits; moreover, there is an inverse relationship between the achievable sampling rate and the bit depth. In this paper, we investigate an alternative CS approach that shifts the emphasis from the sampling rate to the number of bits per measurement. In particular, we explore the extreme case of 1-bit CS measurements, which capture just their sign. Our results come in two flavors. First, we consider ideal reconstruction from noiseless 1-bit measurements and provide a lower bound on the best achievable reconstruction error. We also demonstrate that i.i.d. random Gaussian matrices describe measurement mappings achieving, with overwhelming probability, nearly optimal error decay. Next, we consider reconstruction robustness to measurement errors and noise and introduce the Binary @math -Stable Embedding (B @math SE) property, which characterizes the robustness measurement process to sign changes. We show the same class of matrices that provide almost optimal noiseless performance also enable such a robust mapping. On the practical side, we introduce the Binary Iterative Hard Thresholding (BIHT) algorithm for signal reconstruction from 1-bit measurements that offers state-of-the-art performance. A space-variant interpolation is required to compensate for the migration of signal energy through range resolution cells when processing synthetic aperture radar (SAR) data, using either the classical range Doppler (R D) algorithm or related frequency domain techniques. In general, interpolation requires significant computation time, and leads to loss of image quality, especially in the complex image. The new chirp scaling algorithm avoids interpolation, yet performs range cell migration correction accurately. The algorithm requires only complex multiplies and Fourier transforms to implement, is inherently phase preserving, and is suitable for wide-swath, large-beamwidth, and large-squint applications. This paper describes the chirp scaling algorithm, summarizes simulation results, presents imagery processed with the algorithm, and reviews quantitative measures of its performance. Based on quantitative comparison, the chirp scaling algorithm provides image quality equal to or better than the precision range Doppler processor. Over the range of parameters tested, image quality results approach the theoretical limit, as defined by the system bandwidth. > Compressive sampling (CS), also called compressed sensing, entails making observations of an unknown signal by projecting it onto random vectors. Recent theoretical results show that if the signal is sparse (or nearly sparse) in some basis, then with high probability such observations essentially encode the salient information in the signal. Further, the signal can be reconstructed from these "random projections," even when the number of observations is far less than the ambient signal dimension. The provable success of CS for signal reconstruction motivates the study of its potential in other applications. This paper investigates the utility of CS projection observations for signal classification (more specifically, m-ary hypothesis testing). Theoretical error bounds are derived and verified with several simulations.