An Accurate Sparse SAR Imaging Method for Enhancing Region-Based Features Via Nonconvex and TV Regularization

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, 1 optimization induces sparsity the most effectively, and the 1 -norm penalty is usually combined with the total variation norm (TV-norm) penalty to construct a compound regularizer in order to enhance the pointbased features as well as the region-based features. However, as a convex optimizer, the analytic solution of 1 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 1 regularization, nonconvex regularization can reduce the average relative bias from 10.88% to 0.25%; compared with the matched filtering method and 1 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.

Widely Distributed Radar Imaging: Unmediated ADMM Based Approach

“…1) Convergence rate: it can be assessed by the number of iterations needed to reach the stopping criteria that is defined identically for both algorithms. 2) Computational complexity: the main computational burden of both algorithms lies in the local image updates (11) and (17), where the matrix inversion term is present. Due to their large size, the measurement matrices A q are realized through matrix operators based on twodimensional non-uniform Fast Fourier transform (2D NuFFT) [28].…”

“…Moreover, the inversion step is carried out numerically using CG as mentioned earlier. Thus, while the complexity of both algorithms seems to be equivalent, the convergence of CG highly depends on the other variables in the update formulas (11) and (17). As a result, the comparison solely in terms of the number of iterations is not indicative since a single iteration in each of the algorithms may realize a different cost.…”

“…Nevertheless, the imaging involves a dictionary search process that is computationally cumbersome [13]. The other approach is composite imaging [14]- [17] in which the full aperture is divided into sub-apertures within which the point scattering model holds. Respectively, images of each sub-aperture are formed through regularized optimization exploiting specific features such as sparsity.…”

Sparse SAR Imaging and Quantitative Evaluation Based on Nonconvex and TV Regularization

“…Given the above two problems, we linearly combine the nonconvex penalty and the TV-norm penalty as a compound regularizer, generating the following nonconvex and TV regularization model [18]:…”

“…The above research shows that TV regularization can result in reconstructions with emphasized piecewise-constant features. Therefore, in a recently submitted contribution, we have proposed to linearly combine the nonconvex penalty and the TV-norm penalty as a compound regularizer in the imaging model, called nonconvex and TV regularization, which can not only reduce the bias caused by L 1 regularization but also enhance point-based and region-based features [18,19].…”