Abstract
With the rapid development of compressed sensing theories and applications, sparse signal processing has been widely used in synthetic aperture radar (SAR) imaging during the recent years. As an efficient tool for sparse reconstruction, ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> optimization induces sparsity the most effectively, and the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm penalty is usually combined with the total variation norm (TV-norm) penalty to construct a compound regularizer in order to enhance the point-based features as well as the region-based features. However, as a convex optimizer, the analytic solution of ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization-based sparse signal reconstruction is usually a biased estimation. Aiming at this issue, in this article, we quantitatively analyzed the variation of reconstruction bias with respect to the complex reflectivity of targets, the undersampling ratio and the noise power. In order to reduce the bias effect and improve the reconstruction accuracy, we adopted the nonconvex regularization-based sparse SAR imaging method with a nonconvex penalty family. Furthermore, we linearly combined the nonconvex penalty and the TV-norm penalty to form a compound regularizer in the imaging model, which can improve the reconstruction accuracy of distributed targets and maintain the continuity of the backscattering coefficient. Simulation results showed that compared with ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization, nonconvex regularization can reduce the average relative bias from 10.88% to 0.25%; compared with the matched filtering method and ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and TV regularization, nonconvex & TV regularization can reduce the variance of the uniformly distributed targets by 80% without losing of reconstruction accuracy. Experiments on Gaofen-3 SAR data are also exploited to verify the effectiveness of the proposed method.
Highlights
S YNTHETIC aperture radar (SAR) is an active remote sensing technology, which carries on a moving platform, Manuscript received March 2, 2020; revised August 22, 2020 and October 9, 2020; accepted October 25, 2020
It can be seen that the relative bias of targets becomes larger as the amplitude of reflectivity decreases for 1 regularization, which means that the bias effect has a greater impact on weak targets
Nonconvex regularization can control the relative bias at a low level
Summary
S YNTHETIC aperture radar (SAR) is an active remote sensing technology, which carries on a moving platform, Manuscript received March 2, 2020; revised August 22, 2020 and October 9, 2020; accepted October 25, 2020. Due to the radar resolving theory and Nyquist–Shannon sampling theorem, improvement of SAR system performance usually comes with the remarkably increased sampling data amount, and brings complexities to the system design and implementation [1]. Sparse signal processing is widely used in SAR imaging with the development of compressed sensing and related theories, which shows that a sparse signal can be effectively reconstructed with much fewer samples than that required by Nyquist–Shannon sampling theorem [2],[3]. For full sampling systems, sparse signal processing is beneficial in terms of improving reconstruction performance. Sparse microwave imaging works effectively in multiple SAR modes, including stripmap SAR, ScanSAR, spotlight SAR, and TOPS SAR [4]–[6]
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