Analysis and suppression of bias effect in sparse SAR imaging

Three-dimensional (3D) synthetic aperture radar (SAR) imaging provides complete 3D spatial information, which has been used in environmental monitoring in recent years. Compared with matched filtering (MF) algorithms, the regularization technique can improve image quality. However, due to the substantial computational cost, the existing observation-matrix-based sparse imaging algorithm is difficult to apply to large-scene and 3D reconstructions. Therefore, in this paper, novel 3D sparse reconstruction algorithms with generalized Lq-regularization are proposed. First, we combine majorization–minimization (MM) and L1 regularization (MM-L1) to improve SAR image quality. Next, we combine MM and L1/2 regularization (MM-L1/2) to achieve high-quality 3D images. Then, we present the algorithm which combines MM and L0 regularization (MM-L0) to obtain 3D images. Finally, we present a generalized MM-Lq algorithm (GMM-Lq) for sparse SAR imaging problems with arbitrary q0≤q≤1 values. The proposed algorithm can improve the performance of 3D SAR images, compared with existing regularization techniques, and effectively reduce the amount of calculation needed. Additionally, the reconstructed complex image retains the phase information, which makes the reconstructed SAR image still suitable for interferometry applications. Simulation and experimental results verify the effectiveness of the algorithms.

Synthetic aperture radar (SAR) is widely used for ground observations owing to its all-weather and all-time capabilities. Sparse SAR reconstruction imaging, which can enhance SAR imaging performance, has emerged as a significant research area. The traditional sparse SAR reconstruction imaging method was successfully applied to raw SAR data processing. However, the computational complexity makes sparse reconstruction imaging difficult for large scenes. Meanwhile, because raw data are usually kept confidential, only limited data are available. To address the issue of how to use publicly available complex image data for sparse reconstruction and effectively improve image quality, this study proposes a joint L1- and F-norm edge-preservation-based sparse SAR reconstruction algorithm for complex images. The algorithm uses the gradient descent (GD) technique to optimize the L1-norm regularization and reconstruct the overall image information; the iterative soft thresholding algorithm (ISTA) to optimize the F-norm regularization and reconstruct the high-frequency image information; and fuses the two sets of reconstructed information to obtain SAR reconstructed images with characteristics such as edge preservation, clear texture, and high quality. The results show that, compared with traditional matched filtering (MF) imaging results, the joint L1- and F-norm results obtained for complex images have lower sidelobes, higher signal-to-noise ratio, and better target resolution ability; compared with the F-norm-based sparse SAR reconstruction imaging results, the joint L1- and F-norm method provides images with better edge texture clarity.

Sparse signal processing-based Synthetic Aperture Radar (SAR) imaging, also known as sparse SAR imaging, is the main research direction of sparse microwave imaging theory. Compared with a conventional SAR system, sparse SAR imaging radar has significant potential to improve imaging performance. However, because it requires heavy computations, the application of sparse SAR imaging in large-scene recovery has become difficult, which restricts its further applications. Additionally, complex SAR images, rather than raw data, are usually used for data archiving due to a number of reasons such as data copyright and system confidentiality. Therefore, it is worthwhile to study how sparse imaging can be achieved using only Matched Filtering (MF) recovered complex images with less computational cost. GaoFen-3 is China’s first 1-m resolution multi-polarization C-band satellite. It has a high-resolution, wide swath imaging ability and hence plays an important role in disaster monitoring and ocean surveillance applications. In this paper, we introduce a complex image-based sparse SAR imaging method to process GaoFen-3 complex image data and improve image performance. Experimental results show that the sparse imaging results have lower sidelobes, higher signal-toclutter and noise ratio, and better target distinguishing ability compared with inputted images. Additionally, sparse imaging can effectively preserve the statistical distribution and phase information of images that makes the recovered GaoFen-3 sparse image-based applications such as interferometric synthetic aperture radar and constant false alarm ratio detection possible.

Sparse signal processing is widely used in synthetic aperture radar (SAR) imaging with the development of compressed sensing. As a typical sparse reconstruction method, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{1}$</tex> regularization generally causes bias effect. In this paper, we linearly combine the nonconvex penalty and the total variation (TV)-norm penalty as a compound regularizer in the imaging model, which can improve the reconstruction accuracy of targets as well as maintain the continuity of the backscattering coefficient in uniform regions. Simulations and experiments based on real data from Gaofen-3 are performed to verify the effectiveness of the proposed method.

There are two issues in the Sparse Reconstruction (SR) algorithm of Multiple Measurement Vectors (MMV). One is the high computation complexity and the other is that redundant support set can not be effectively removed. In order to improve the efficiency and accuracy of SR algorithm simultaneously for MMV model, a Fast Orthogonal Matching Pursuit algorithm based on Bayesian Test (FOMP-BT) is presented in this paper. Firstly, the total number of iterations and the computation of each iteration are reduced through the new atomic group selection and warm start matrix inversion, thus the efficiency of the algorithm is improved. Secondly, using the idea of the Bayesian test to eliminate redundant support set, the accuracy of reconstruction is improved. Finally, the theoretical analysis of the algorithm is carried out from the aspects of parameter selection and computation complexity. The simulation results show that the proposed algorithm has the advantages of high accuracy, fast speed and good robustness to noise.

The statistical power of cross-over trials can be increased by taking 'baseline' measurements of the outcome variable at the start of each treatment period. Analysis of covariance (ANCOVA), rather than analysis of change scores, takes best advantage of this. However, ANCOVA can give biased treatment effect estimates in observational studies with true baseline imbalance. While in truth balanced, chance baseline imbalance is possible in individual randomized cross-over studies due to their typically small sample size. Although such chance imbalance does not cause biased estimation on average over repeated trials, this simulation study will aim to confirm the appropriateness of ANCOVA when faced with the analysis of data from an individual trial in which chance baseline imbalance is clearly apparent. Randomized cross-over trials were simulated, varying in sample size and the pattern and strength of correlation between repeated measures. Estimates from ANCOVA, change scores, and post-treatment difference were unbiased on average across each set of simulated data sets. ANCOVA and change scores could use baseline information to improve precision, but change scores could also reduce precision if baseline measures were uninformative. Change scores only were correlated with chance within-subject baseline imbalance. All three estimators could be correlated with chance between-subjects imbalance in the first period baseline measurements, the strongest associations being with the post-treatment difference. Consistent results were obtained from a real data example. In conclusion, ANCOVA took best advantage of baseline measures to improve precision, and avoided bias in the widest set of circumstances with chance imbalance in those baseline measures.

Aiming at the problems of synthetic-aperture radar (SAR), such as high sampling rate and vulnerability to noise interference in imaging, a sparse reconstruction algorithm based on approximate observation and L1/2 threshold iteration is proposed in this paper. To solve the problem of the large dimension and high computational complexity of the measurement matrix, a sparse reconstruction model based on approximate observation is constructed, and a threshold iterative algorithm to rapidly solve the L1/2 regularization problem is introduced, which can realize sparse signal reconstruction with fewer sampling data and quickly solve the problem. The simulation results of point targets and the measured data of spaceborne SAR show that compared with the traditional matched filtering algorithm and L1 threshold algorithm based on a two-step iteration, the proposed sparse reconstruction algorithm has a faster iteration speed and improves the image quality.

Uncovering brain activity from magnetoencephalography (MEG) data requires solving an ill-posed inverse problem, greatly confounded by noise, interference, and correlated sources. Sparse reconstruction algorithms, such as Champagne, show great promise in that they provide focal brain activations robust to these confounds. In this paper, we address the technical considerations of statistically thresholding brain images obtained from sparse reconstruction algorithms. The source power distribution of sparse algorithms makes this class of algorithms ill-suited to “conventional” techniques. We propose two non-parametric resampling methods hypothesized to be compatible with sparse algorithms. The first adapts the maximal statistic procedure to sparse reconstruction results and the second departs from the maximal statistic, putting forth a less stringent procedure that protects against spurious peaks. Simulated MEG data and three real data sets are utilized to demonstrate the efficacy of the proposed methods. Two sparse algorithms, Champagne and generalized minimum-current estimation (G-MCE), are compared to two non-sparse algorithms, a variant of minimum-norm estimation, sLORETA, and an adaptive beamformer. The results, in general, demonstrate that the already sparse images obtained from Champagne and G-MCE are further thresholded by both proposed statistical thresholding procedures. While non-sparse algorithms are thresholded by the maximal statistic procedure, they are not made sparse. The work presented here is one of the first attempts to address the problem of statistically thresholding sparse reconstructions, and aims to improve upon this already advantageous and powerful class of algorithm.

Sparse reconstruction of EMT based on compressed sensing and Lp regularization with the split Bregman method

In this paper, a novel synthetic aperture radar (SAR) imaging method based on L 1/2 regularization is proposed. Our method implements SAR imaging from compressed measurements with high resolution, enhanced features, reduced sidelobes and suppressed artifacts. Real SAR data experiments are implemented to demonstrate the outperformance of our method. The experiment results demonstrate that our method needs far below the traditional Nyquist rate to guarantee successful imaging. Compared to the prevalent L 1 regularization-based methods, there is a significant reduction of the sampling rate for SAR imaging. The sampling rate used by our method is about half of the L 1 regularization-based methods in the real SAR data experiments.

Elevation estimation of canopy and ground is one of the main aims in dealing with forest scenario using Synthetic Aperture Radar (SAR) Tomography. Theoretically, SAR Tomography (TomoSAR) provides layover solution, allowing to reconstruct the elevation of the different contributions collapsing in the same resolution cell. TomoSAR is commonly applied on both urban and vegetated areas. Within the latter scenario, one of the most interesting outcomes of TomoSAR is the possibility of separating the canopy and ground, allowing the reconstruction of their height maps. Within this paper, we propose a Deep Learning (DL) based method for TomoSAR. In particular, a neural network was trained for predicting the elevation value of canopy and ground of an area under investigation, based on a stack of SAR fully polarimetric multi-baseline acquisitions. The method uses the Light Detection And Ranging (LiDAR) data as reference and exploit a classification approach. The process was operated on a tropical forest over the TropiSAR2009 test site in Paracou, French Guiana. Testing results on real data are presented showing interesting results.

In synthetic aperture radar (SAR) images, inland water bodies generally appear as dark textures, but due to the interference of thermal noise, speckle noise, and azimuth blur, inland water bodies can be easily confused with weakly scattered areas such as roads, wetlands, and sand. Most of the existing denoising methods have been proposed for removing speckle noise. However, the presence of thermal noise and azimuth blur still makes it difficult to distinguish inland water bodies. The denoising method based on the Doppler spectrum can effectively remove thermal noise, speckle noise, and azimuth blur, but it reduces the resolution, which blurs the contour of the water body, and it is difficult to apply to the detection and processing of small inland water bodies. Fusing a noisy high-resolution image with a low-resolution image with less noise makes it possible to remove the speckle noise and thermal noise of the SAR image while maintaining the edge texture of the water body. Based on the idea of image fusion, sparse representation is used to fuse the original noisy SAR image (HR) and the low-precision image (LR) processed by the denoising algorithm to maximise the use of all the information in HR and LR. According to this idea, an enhancement algorithm for separability of inland water body based on sparse representation is proposed. The experimental results show that the proposed model significantly improves the separability of inland water bodies in SAR images.

In this paper, we investigate the synthetic aperture radar (SAR) imaging problem via sparse atomic norm reconstruction. A stepped-frequency radar operation and a side looking radar is assumed. However, the analysis presented is general, and extensions to other SAR types, scenes and other radar waveforms are straightforward. The atomic norm is formulated and employed as a penalizer for SAR denoising and reconstruction, as a convex problem. The target positions are readily estimated through the peaks of the dual polynomial. Furthermore, due to strong duality in our convex formulation, we show that the target positions are obtained from either the primal or dual problem solution. Through simulations, we demonstrate the advantages of our approach when compared with traditional back-projection imaging and recent sparse reconstruction techniques.

This letter presents a new motion parameter estimation method using synthetic aperture radar (SAR) images based on sparse reconstruction. The method uses orthogonal matching pursuit, which correlates a SAR image with elements in a reference basis. The reconstruction result provides a high-resolution focused image and corresponding motion parameters. It does not require narrow-beamwidth assumption and prior motion information, as compared with the existing method based on matching pursuit. We design the reference basis by theoretically analyzing the performance degradation due to parameter mismatch. We further calculate required position and velocity parameter resolutions in the basis. The calculated resolutions are validated by means of simulations. Imaging examples with real SAR images of a scene acquired over Ottawa, Canada, show the effectiveness of our method.

A directional pursuit algorithm is proposed to reconstruct an unknown sparse signal from noisy measurements. The algorithm offered an iterative update direction for improving the reconstructive accuracy of compressive sensing. Unlike traditional directional pursuit methods which only select the atoms owning higher correlation with the residual signal, the proposed algorithm not only values the higher correlation atoms but also reserves the lower correlation atoms with the residual signal. In the lower correlation atoms, only a few are active which usually impact the reconstructive performance and decide the reconstruction dynamic range of directional pursuit methods. The others are inactive. In order to avoid redundant atoms impacting the reconstructive accuracy, Bayesian hypothesis testing model is used to identify active atoms and eliminate redundant ones. Simulation results of the proposed algorithm show that the reconstructive accuracy and reconstructive dynamic range can indeed be improved. Furthermore, better noisy immunity compared with the traditional directional pursuit methods can be obtained.