Compressed Sensing Radar Imaging With Compensation of Observation Position Error

Image formation algorithms in a variety of applications have explicit or implicit dependence on a mathematical model of the observation process. Inaccuracies in the observation model may cause various degradations and artifacts in the reconstructed images. The application of interest in this paper is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data, which cause defocusing of the reconstructed images. Particularly focusing on imaging of fields that admit a sparse representation, we propose a sparsity-driven method for joint SAR imaging and phase error correction. Phase error correction is performed during the image formation process. The problem is set up as an optimization problem in a nonquadratic regularization-based framework. The method involves an iterative algorithm, where each iteration of which consists of consecutive steps of image formation and model error correction. Experimental results show the effectiveness of the approach for various types of phase errors, as well as the improvements that it provides over existing techniques for model error compensation in SAR.

Synthetic aperture radar (SAR) is a kind of high-resolution imaging radar, which can work in any weather conditions and is often used for target positioning. Airborne SAR has the advantages of flexible scanning geometry and high spatial resolution compared with Spaceborne SAR, but the quality of SAR image and positioning accuracy is affected by air turbulence and mechanical vibration. In practical applications, it is vital to improve Airborne SAR’s geometric positioning accuracy without ground control points or other reference image information. When positioning a single SAR image with long-range, the Earth surface model is often used as an additional equation to solve the Range-Doppler (RD) model. However, the Earth surface equation is difficult to solve the target height accurately. This study proposed an Airborne SAR target positioning methodology based on a local linear approximation of the Earth surface equation. The proposed local Linear RD (L-RD) model establishes a linear constraint of the local elevation, and the iterative algorithm converges rapidly. To further improve the efficiency of geolocation, we propose a method to directly obtain the initial geolocation used for the iteration based on the geometric relationship. An iterative framework is also proposed to enhance positioning accuracy when DEM is available. The experimental results show that the proposed method can significantly improve the positioning accuracy and reliability of Airborne SAR positioning without control points compared to other methods.

Cropland classification can be used to monitor cropland distribution and its change over time. In this letter, a new superpixel-based cropland classification method is proposed for synthetic aperture radar (SAR) imagery through the integration of statistical texture, polarization, and spatial information. First, the method combines random forest algorithm and superpixels, which are generated using simple linear iterative clustering algorithm with polarization features of Pauli decomposition and spatial information. Superpixel-based spatial context information is used to reduce the influence of coherent speckle and misclassification in cropland blocks. Second, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$G^{0}$ </tex-math></inline-formula> statistical texture feature is used to reduce the interference of background targets such as woodland in cropland classification. Comparison experiments of different methods using C-band airborne SAR (AIRSAR) polarimetric data acquired in early July show that the proposed method has better classification performance, with an overall accuracy of 88.62%. The classification accuracy of corn and soybean is above 95% and 91%, respectively. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$G^{0}$ </tex-math></inline-formula> statistical texture feature is helpful to eliminate woodland that may cause crop misclassification using single-date SAR image.

In the past decade, the compressive sensing (CS) based ISAR imaging methods have gained much interest due to the capability of obtaining high-quality images with under-sampled data. However, both the performance and the application of CS ISAR imaging methods are limited by sparse representations and iterative reconstruction algorithms where the former may be hard to find and the latter may lead to low imaging efficiency. The deep-network (DN) based image reconstruction methods appeared in recent years have been shown to be able to dramatically reduce the computational complexity and ensure the image reconstruction at the same time. The Deep-ADMM-Net (DAN) is a network constructed by iterative steps of the traditional optimization algorithm, Alternating Direction Method of Multipliers (ADMM). The mainly characteristic of DAN is that it is interpretable and efficient. We propose a DAN based ISAR imaging method. The well trained DAN can reconstruct high-quality ISAR image using much fewer measurements than CS based imaging methods. Experimental results show that our proposed imaging method is superior to the existing CS method in both image reconstruction quality and computational efficiency

A novel autofocus method for synthetic aperture radar (SAR) image is studied. Based on a quadratic model for the phase error within each sub-area (narrow strip × sub-aperture) after a wide range swath is subdivided into narrow range strips and long azimuth aperture into sub-apertures, an objective function for estimation of the error is derived through the principle of minimum entropy. There is only one unknown variable in the function. With the Chebyshev approximation, the function is approximated as a polynomial, and the unknown is then solved using the method of series reversion. Curve-fitting methods are applied to estimate phase error for an entire scene of the full-swath by full-aperture. Through simulations, the proposed method is applied to restore the defocused SAR imagery that is well focused. The restored and original images are almost identical qualitatively and quantitatively. Next, the method is implemented into an existing SAR data processor. Two sets of SAR raw data at X- and Ku-bands are processed and two images are formed. Well-focused and high-resolution images from plain and rugged terrain are obtained even without the use of ancillary attitude data of the airborne SAR platform. Thus, the studied method is verified.

Synthetic Aperture Radars (SAR) provide high resolution ground images by utilizing the aircraft motion to synthesize a large aperture. The presence of residual phase error in the SAR images causes defocusing in the images. Autofocus algorithm compensates these phase errors to obtain a focused image. In most scenarios a priori information about the type of phase error is known which can be effectively utilized in autofocus techniques. The paper proposes a new autofocus algorithm which is based on Wiener filter theory and implements a multistage Wiener filter to compensate the phase error in SAR images.

Radar coincidence imaging is a new method for high-resolution staring imaging. First, the mathematical model is constructed. Second, the theoretical error for radar coincidence imaging in the presence of noise is derived using the parametric imaging method. Third, the factors that affect the error are analyzed. Fourth, the sparse reconstruction algorithm is used to perform numerical simulations of radar coincidence imaging with different parameters. Finally, the effects of signal bandwidth, array configuration, size of the imaging unit, and target complexity on image error in the presence of noise are discussed. This study provides the theoretical framework for parameters selection and SNR requirements for radar coincidence imaging systems.

Multiple-input multiple-output (MIMO) radar uses waveform diversity technology to form a virtual aperture to improve the azimuth resolution of forward-looking imaging. However, the super-resolution imaging capability of MIMO radar is limited, and the resolution can only be doubled compared with the real aperture. In the radar forward-looking image, compared with the whole imaging scene, the target only occupies a small part. This sparsity of the target distribution provides the feasibility of applying the compressed sensing (CS) method to MIMO radar to further improve the forward-looking imaging resolution. At the same time, the forward-looking imaging method for a MIMO radar based on CS has the ability to perform single snapshot imaging, which avoids the problem of a motion supplement. However, the strong noise in the radar echo poses a challenge to the imaging method based on CS. Inspired by the low-rank properties of the received radar echoes and the generated images, and considering the existing information about sparse target distribution, a forward-looking super-resolution imaging model of a MIMO radar that combines sparse and double low-rank constraints is established to overcome strong noise and achieve robust forward-looking super-resolution imaging. In order to solve the multiple optimization problem, a forward-looking image reconstruction method based on the augmented Lagrangian multiplier (ALM) is proposed within the framework of the alternating direction multiplier method (ADMM). Finally, the results of the simulation and the measurement data show that the proposed method is quite effective at improving the azimuth resolution and robustness of forward-looking radar imaging compared with other existing methods.

Two swaths of airborne synthetic aperture radar (AIRSAR) imagery, acquired over the southern Huon Peninsula, Papua New Guinea, have been digitally merged with aerial photogrammetric topography and with Hawaii MR] acoustic side‐scan imagery and bathymetry of the adjacent seabed of Huon Gulf. This example of land‐sea integration provides a means of examining relationships between tectonic lineaments and sediment transport pathways on land and on the subjacent seabed. Imaging methods and geometries dictate both the regions covered and the information content of the data. The principal limitations in merging the two data sets arise because the coastal and inner shelf zone, in water depths less than 500 m, is inaccessible to the imaging techniques that were used. Indirect methods allow some inferences to be made about the geomorphology of this zone, using surface sound channel data and sea surface imagery. The area examined is part of an active tectonic collision zone in which the northern margin of the Australian plate is being subducted beneath the South Bismarck plate. The edge of the South Bismarck plate has been uplifted 4,000 m since the late Pliocene, forming the Finisterre Range on Huon Peninsula. The record of relative emergence and submergence is seen in subaerially exposed Quaternary marine sediments and in drowned carbonate reefs. The merged radar and sonar imagery clearly indicate rapid erosion and deformation, both on land and under water. The imagery shows details of sediment transport and depositional systems, which are generating large terrestrial fluvial/alluvial plains, coastal fan deltas, and submarine channel deposystems. Fault structures and outcrops of bedrock units are clearly delineated both on land and on the seabed. These observations help explain patterns of onshore and submarine outcrops in terms of interactions between modern offshore sedimentation patterns and progressive deformation.

High-resolution radar imaging has to be accomplished within the constraints of aperture size, frequency, and acquisition time. To achieve effective and reliable imaging, we introduce a compressed sensing (CS) technology to spread spectrum through-the-wall radar imaging. Using the sparseness of the spread spectrum through-the-wall radar echo in the correlation domain and the sparsity of the target information in the imaging region, the feasibility of CS technology for reducing the number of observation points and the number of samples per observation point is verified. Moreover, considering the high sensitivity of CS technology to clutter, receiver cancellation is adopted to remove the strong clutter information present in echo signals. The results of numerical simulations show that CS technology can provide very efficient sampling, thereby significantly reducing the amount of data required. Compared to back-projection imaging based on traditional sampling technology, the proposed CS technique can obtain almost the same satisfactory resolution and quality imaging results using only 0.72% of the total data. This will reduce the hardware costs and significantly shorten the data-acquisition and data-transfer times.

This paper presents a visual servoing method for a redundant manipulator to control quickly and accurately by image error in a complicated environment. The proposed approach combines two parts, one is position-based visual servoing, and another is avoiding obstacles by using virtual repulsive torque. The image features are found and mapped by Oriented FAST and Rotated BRIEF (ORB) and the image errors are calculated. Furthermore, the object pose is estimated in the world coordinate by the image errors and the current pose of the manipulator and the target EOAT pose compute will be obtained. After confirming the EOAT pose, this method introduces a virtual repulsive torque for solving generalized inverse kinematics problems by analytical and numerical methods. The proposed approach uses the property of the redundant manipulator to maintain the distance between links and obstacles. For the applicability, we transform the programs to the nodes and use Robot Operating System as the core to build the communication protocol for exchanging information. The validity and efficiency of the proposed method are measured in simulations, by which it verifies that the method is not only feasible to constrained motions but also has good performances in collision avoidance.

Recently, compressed sensing (CS) has been widely used in ground penetrating radar (GPR) imaging due to its low sampling tune, high quality performance and high quality imaging results in underground imaging. However, for densely distributed underground multi-target, the error of GPR imaging based on CS is large. So, this paper proposes a filter matrix, which can effectively reduce the energy of B-scan hyperbolic arms, increase the hyperbolic apex energy, and reduce the error of GPR imaging based on CS in densely distributed multi-target environment. The algorithm also takes into account the distance between the antenna and the ground. At first, a method of the normalized is used to calculate the echo data. Then the filter matrix designed in this paper is used. Experimental results present that the filter matrix can effectively reduce the imaging error in multi-target environment.

An iterative convex optimization algorithm for wide scanning sparse conformal array synthesis is proposed. Combined with the compressed sensing (CS) theory, the proposed method is used to find the optimal element position for multiple scanning angle patterns by using cooperative synthesis strategy. The iterative algorithm first uses Euler’s calculation transformation to overcome the problem that the element pattern cannot be superimposed in a unified coordinate system due to the different distribution positions of the array elements. Secondly, the non-convex sparsity problem of circular-arc array with limited mainlobe width is transformed into a convex form with minimized l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> norm. Several numerical simulations are operated to validate the correctness and effectiveness of the proposed algorithm.

The most common technique for generating B-mode ultrasound (US) images is delay-and-sum (DAS) beamforming, where the signals received at the transducer array are sampled before an appropriate delay is applied. This necessitates sampling rates exceeding the Nyquist rate and the use of a large number of antenna elements to ensure sufficient image quality. Recently, we proposed methods to reduce the sampling rate and the array size relying on image recovery using iterative algorithms based on compressed sensing (CS) and the finite rate of innovation (FRI) frameworks. Iterative algorithms typically require a large number of iterations, making them difficult to use in real time. In this article, we propose a reconstruction method from sub-Nyquist samples in the time and spatial domain, which is based on unfolding the iterative shrinkage thresholding algorithm (ISTA), resulting in an efficient and interpretable deep network. The inputs to our network are the subsampled beamformed signals after summation and delay in the frequency domain, requiring only a subset of the US signal to be stored for recovery. Our method allows reducing the number of array elements, sampling rate, and computational time while ensuring high-quality imaging performance. Using in vivo data, we demonstrate that the proposed method yields high-quality images while reducing the data volume traditionally used up to 36 times. In terms of image resolution and contrast, our technique outperforms previously suggested methods as well as DAS and minimum-variance (MV) beamforming, paving the way to real-time applicable recovery methods.

In this work we study the problem of focusing Synthetic Aperture Radar (SAR) images by means of Compressive Sensing (CS). The presented technique is introduced as an alternative to the traditional focusing methods, suggesting new modes for data acquisition in a more efficient configurations or on-board processing in case of spaceborne sensors. In this paper the method is tested on both simulated and real images acquired by a Ground Based Synthetic Aperture Radar (GB-SAR), for which images of reduced size can be generated with no difficulty. Results of comparison of CS processing with an exact focusing algorithm are shown in terms of root mean square error of amplitude and phase as a function of the number of focused targets and undersampling of the acquisition lines. Coherence of a CS-processed couple of images is also evaluated. The purpose of the paper is to show the potential of CS applied to SAR systems, regardless (at the moment) of the efficiency in computational load. In particular, we show that the image can be reconstructed without loss of resolution after dropping a fair percentage of the received pulses.