We introduce a maximum a posteriori (MAP) algorithm and a sparse learning via iterative minimization (SLIM)
algorithm to synthetic aperture radar (SAR) imaging. Both MAP and SLIM are sparse signal recovery algorithms
with excellent sidelobe suppression and high resolution properties. The former cyclically maximizes the a
posteriori probability density function for a given sparsity promoting prior, while the latter cyclically minimizes
a regularized least squares cost function. We show how MAP and SLIM can be adapted to the SAR imaging
application and used to enhance the image quality. We evaluate the performance of MAP and SLIM using the
simulated complex-valued backscattered data from a backhoe vehicle. The numerical results show that both MAP
and SLIM satisfactorily suppress the sidelobes and yield higher resolution than the conventional matched filter
or delay-and-sum (DAS) approach. MAP and SLIM outperform the widely used compressive sampling matching
pursuit (CoSaMP) algorithm, which requires the delicate choice of user parameters. Compared with the recently
developed iterative adaptive approach (IAA), MAP and SLIM are computationally more efficient, especially with
the help of fast Fourier transform (FFT). Also, the a posteriori distribution given by the algorithms provides us
with a basis for the analysis of the statistical properties of the SAR image pixels.
Probing waveform synthesis and receive filter design play crucial roles in achievable performance for active
sensing applications, including radar, sonar, and medical imaging. We focus herein on conventional single-input
single-output (SISO) radar systems. A flexible receive filter design approach, at the costs of lower signal-to-noise
ratio (SNR) and higher computational complexity, can be used to compensate for missing features of
the probing waveforms. A well synthesized waveform, meaning one with good autocorrelation properties, can
reduce computational burden at the receiver and improve performance. Herein, we will highlight the interplay
between waveform synthesis and receiver design. We will review a novel, cyclic approach to waveform design, and
then compare the merit factors of these waveforms to other well-known sequences. In our comparisons, we will
consider chirp, Frank, Golomb, and P4 sequences. Furthermore, we will overview several advanced techniques for
receiver design, including data-independent instrumental variables (IV) filters, a data-adaptive iterative adaptive
approach (IAA), and a data-adaptive Sparse Bayesian Learning (SBL) algorithm. We will show how these designs
can significantly outperform conventional matched filter (MF) techniques for range compression as well as for
range-Doppler imaging.
We consider sidelobe reduction and resolution enhancement in synthetic aperture radar (SAR) imaging via an
iterative adaptive approach (IAA) and a sparse Bayesian learning (SBL) method. The nonparametric weighted
least squares based IAA algorithm is a robust and user parameter-free adaptive approach originally proposed
for array processing. We show that it can be used to form enhanced SAR images as well. SBL has been used as
a sparse signal recovery algorithm for compressed sensing. It has been shown in the literature that SBL is easy
to use and can recover sparse signals more accurately than the l 1 based optimization approaches, which require
delicate choice of the user parameter. We consider using a modified expectation maximization (EM) based SBL
algorithm, referred to as SBL-1, which is based on a three-stage hierarchical Bayesian model. SBL-1 is not only
more accurate than benchmark SBL algorithms, but also converges faster. SBL-1 is used to further enhance
the resolution of the SAR images formed by IAA. Both IAA and SBL-1 are shown to be effective, requiring
only a limited number of iterations, and have no need for polar-to-Cartesian interpolation of the SAR collected
data. This paper characterizes the achievable performance of these two approaches by processing the complex
backscatter data from both a sparse case study and a backhoe vehicle in free space with different aperture sizes.
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