Omega-K Algorithm Research Articles

A Robust Track Estimation Method for Airborne SAR Based on Weak Navigation Information and Additional Envelope Errors

As miniaturization technology has progressed, Synthetic Aperture Radar (SAR) can now be mounted on Unmanned Aerial Vehicles (UAVs) to carry out observational tasks. Influenced by airflow, UAVs inevitably experience deviations or vibrations during flight. In the context of cost constraints, the precision of the measurement equipment onboard UAVs may be relatively low. Nonetheless, high-resolution imaging demands more accurate track information. It is therefore of great importance to estimate high-precision tracks in the presence of both motion and measurement errors. This paper presents a robust track estimation method for airborne SAR that makes use of both envelope and phase errors. Firstly, weak navigation information is employed for motion compensation, which reduces a significant portion of the motion error. Subsequently, the track is initially estimated using additional envelope errors introduced by the Extended Omega-K (EOK) algorithm. The track is then refined using a phase-based approach. Furthermore, this paper presents the calculation method of the compensated component for each target and provides an analysis of accuracy from both theoretical and simulation perspectives. The track estimation and imaging results in the simulations and real data experiments validate the effectiveness of the proposed method, with an estimation accuracy of real data experiments within 5 cm.

An Improved Omega-K Algorithm for Squinted SAR With Curved Trajectory

An Improved Omega-K Algorithm for Squinted SAR With Curved Trajectory

Doppler Factor in the Omega-k Algorithm for Pulsed and Continuous Wave Synthetic Aperture Radar Raw Data Processing

Synthetic aperture radar (SAR) raw data do not have a direct application; therefore, SAR raw signal processing algorithms are used to generate images that are used for various required applications. Currently, there are several algorithms focusing SAR raw data such as the range-Doppler algorithm, Chirp Scaling algorithm, and Omega-k algorithm, with these algorithms being the most used and traditional in SAR raw signal processing. The most prominent algorithm that operates in the frequency domain for focusing SAR raw data obtained by a synthetic aperture radar with large synthetic apertures is the Omega-k algorithm, which operates in the two-dimensional frequency domain; therefore, in this paper, we used the Omega-k algorithm to produce SAR images and modify the Omega-k algorithm by adding the Doppler factor to improve the accuracy of SAR raw data processing obtained by the continuous wave and pulsed frequency modulated linear frequency modulated radar system from the surfaces of interest. On the other hand, for the case of unmanned aerial vehicle-borne linear frequency modulated continuous wave (LFM-CW) SAR systems, we added motion compensation to the modified Omega-k algorithm. Finally, the testing and validation of the developed Omega-k algorithm used simulated and real SAR raw data for both pulsed synthetic aperture and continuous wave radars. The real SAR raw data used for the validation of the modified Omega-k algorithm were the raw data obtained by the micro advanced synthetic aperture radar (MicroASAR) system, which is an LFM-CW synthetic aperture radar installed on board an unmanned aerial system and the raw data obtained by European remote sensing (ERS-2) satellite with a synthetic aperture radar installed.

Quantum range-migration-algorithm for synthetic aperture radar applications

The 3D range-migration algorithm (RMA) and its 2D equivalent, the omega-k algorithm, are employed in a wide range of applications where reconstruction of synthetic aperture data is required, from satellite radar imaging of planets over seismic imaging of the earth crust, down to phased-array ultrasound and ultrasonic application, and recently in-line synthetic aperture radar for non-destructive testing. These algorithms are based on Fourier transforms and share their time-complexity. This limits highly-resolved measurement data to be processed at high speeds which would be advantageous for modern production feed lines. In this publication, we present the development and implementation of the RMA on a quantum computer that scales favourably compared to the time complexity of the classical RMA. We compare reconstruction results of simulated and measured data of the classical and quantum RMA. Hereby, the quantum RMA is run on a quantum simulator backend as well as on IBM’s Q System One quantum computer. The results show that real world applications and testing tasks may benefit from future quantum computers.

Omega-K beamforming: Practical ramifications of alternative formulations.

The Omega-K algorithm is widely used for creating imagery from synthetic aperture sonar and radar data. In early literature related to Omega-K beamforming, two alternative forms of the algorithm exist: one in which a critical matched-filtering stage is applied before Stolt-mapping and one in which it is applied after. The former was adopted as the standard approach in both fields. In the present study, it is demonstrated that applying the matched-filter prior to Stolt-mapping has the potential to alias acoustic energy associated with wide aperture angles, causing artifacts in imagery, whereas the alternative formulation avoids these artifacts.

Aperture Synthesis With Digital Array Radars and Covariant Change of Wavenumber Variables

Attributes of digital array radars are leveraged in enhancements of wideband frequency-wavenumber (omega-k) methods to achieve 1) single-pulse, short-range imaging from a stationary array; 2) single-pulse, all-range, high-density, digital beamforming-on-receive from a stationary array; 3) multiple-pulse aperture synthesis for short-range imaging with sensor movement; and 4) multiple-pulse inverse aperture synthesis for long-range imaging with tracked object movement. Modifications to conventional omega-k algorithms used in synthetic aperture radar are introduced to accommodate antenna element level data, real array element spacing, large scene size and small array size (compared to scene size). Large scene size with k-space processing is handled by a novel Huygens-Fresnel transfer function that does not fully rely on zero-padding to resolve array and scene size mismatch. Aperture synthesis with generalized pulse-to-pulse sensor-step operations is supported. Connections between omega-k wavenumber migration and a covariant change of variables transform associated with Dirac's spectral models of free and scattered electromagnetic fields are established.

A Modified Range Model and Extended Omega-K Algorithm for High-Speed-High-Squint SAR With Curved Trajectory

Accurate range model with acceleration, the coupling phase terms, and spatial-variant (SV) Doppler parameters are the main issues to be solved in high-speed-high-squint SAR (HSHS-SAR) with a curved trajectory. For these issues, an extended Omega-K (EOK) algorithm is developed in this paper. The proposed EOK algorithm mainly includes the following four aspects. Firstly, a modified range model (AMRM) considering three-dimension acceleration for a curved trajectory is established. Then, the coupling between the range and azimuth direction is removed by the modified Stolt mapping (MSM). Subsequently, an improved high-order spatial-variant (SV) phase correction approach is derived to eliminate the azimuth dependence of Doppler parameters. Finally, in order to avoid zeros-padding operation, the proposed method focuses on the sub-aperture data in the range time and azimuth frequency domain through data aligning processing. The experimental results of both simulation and real data verify the effectiveness of the proposed method.

Translational-Invariant Ultrahigh-Resolution Spaceborne Bistatic SAR Focusing and Image Coordinate Analysis Using Bistatic Polynomial Model

We have proposed a novel process flow for translational-invariant (TI) and ultrahigh-resolution (UHR) bistatic synthetic aperture radar (BSAR) operations, wherein a UHR BSAR image is obtained via coherent integration of sub-aperture images, and its two-dimensional (2D) coordinates are then interpreted. The main contributions of the proposed method are as follows. First, to address additional aliasing of the TI BSAR spectrum after sub-aperture division, linear range walk compensation and its restoration are subsequently performed. This efficiently extends the duration of the Doppler domain after sub-aperture division, accommodating the skewed shape of the TI BSAR spectrum. Second, spatial-variant focusing is achieved via the bistatic polynomial omega-K algorithm (BP-OKA), for which a key consideration is highlighted to perform BP-OKA in the sub-image integration process. In its absence, the same scatterers appeared at different positions in each sub-aperture image, causing failure of coherent accumulation. Finally, to retrieve the range–azimuth coordinates of targets within an illuminated scene, we established a high-order equation using bistatic polynomials, and the 2D image coordinates of targets were determined by solving the equation. This new concept is fully compatible with the proposed BP-OKA and can be used in various spaceborne TI BSAR scenarios. All these contributions were verified using numerical simulations. Accordingly, the proposed processing flow can provide focused SAR images with accurate image coordinate interpretations for TI and UHR BSAR operations.

A Novel Airborne SAR Imaging Method Based on Modified Omega-K Algorithm

A Novel Airborne SAR Imaging Method Based on Modified Omega-K Algorithm

Deep Learning Approach for Object Classification on Raw and Reconstructed GBSAR Data

The availability of low-cost microwave components today enables the development of various high-frequency sensors and radars, including Ground-based Synthetic Aperture Radar (GBSAR) systems. Similar to optical images, radar images generated by applying a reconstruction algorithm on raw GBSAR data can also be used in object classification. The reconstruction algorithm provides an interpretable representation of the observed scene, but may also negatively influence the integrity of obtained raw data due to applied approximations. In order to quantify this effect, we compare the results of a conventional computer vision architecture, ResNet18, trained on reconstructed images versus one trained on raw data. In this process, we focus on the task of multi-label classification and describe the crucial architectural modifications that are necessary to process raw data successfully. The experiments are performed on a novel multi-object dataset RealSAR obtained using a newly developed 24 GHz (GBSAR) system where the radar images in the dataset are reconstructed using the Omega-k algorithm applied to raw data. Experimental results show that the model trained on raw data consistently outperforms the image-based model. We provide a thorough analysis of both approaches across hyperparameters related to model pretraining and the size of the training dataset. This, in conclusion, shows how processing raw data provides overall better classification accuracy, it is inherently faster since there is no need for image reconstruction and it is therefore useful tool in industrial GBSAR applications where processing speed is critical.

Omega-K Algorithm Using Plane Wave Approximation for Forward-Looking Imaging Radar

We propose an Omega-K algorithm that uses plane wave approximation for image formation in forward-looking imaging radar (FIRA) with the multi-input/double-output configuration. We assume that each of the transmitting antennas is located at the center of the receiving antenna array by applying a virtual antenna array. Then, we solve numerical equations in an approximation of the plane wave with the direction normal to the antenna array. Finally, we can obtain an image by proceeding with the following steps in order: the matched filtering, Stolt interpolation, two-dimensional inverse fast Fourier transform, phase compensation, image registration, and image merging. The performance of the proposed algorithm is verified through a simulation and a real experiment with neighboring targets. The results show that the proposed Omega-K algorithm with plane wave approximation can be successfully applied to FIRA systems with bistatic synthetic aperture radar configuration.

다항식 기반 오메가-케이 알고리즘을 이용한 곡선기하에서의 고해상도 바이스태틱 SAR 영상생성에 대한 연구

In this study, we propose a high-resolution synthetic aperture radar (SAR) imaging method for curved-orbit geometry in bistatic configurations with spatially separated transmitter and receiver. To accommodate large curved-path and bistatic configuration properties, we first formulate a B-SAR signal using a polynomial range model and derive its two-dimensional (2D) phase spectrum. Next, we extend the basic concept of the typical omega-K algorithm (OKA) for B-SAR by focusing on the polynomial range model, referred to as polynomial-OKA (P-OKA), enabling us to provide focused SAR images in curved-path and bistatic configurations. Using point target simulations, we verified the efficacy of the proposed P-OKA, where fully focused high-resolution B-SAR images were obtained in various curved-path scenarios.

Omega-KA-Net: A SAR Ground Moving Target Imaging Network Based on Trainable Omega-K Algorithm and Sparse Optimization

The ground moving target (GMT) is defocused due to unknown motion parameters in synthetic aperture radar (SAR) imaging. Although the conventional Omega-K algorithm (Omega-KA) has been proven to be applicable for GMT imaging, its disadvantages are slow imaging speed, obvious sidelobe interference, and high computational complexity. To solve the above problems, a SAR-GMT imaging network is proposed based on trainable Omega-KA and sparse optimization. Specifically, we propose a two-dimensional (2-D) sparse imaging model deducted from the Omega-KA focusing process. Then, a recurrent neural network (RNN) based on an iterative optimization algorithm is built to learn the trainable parameters of Omega-KA by an off-line supervised training method, and the solving process of the sparse imaging model is mapped to each layer of the RNN. The proposed trainable Omega-KA network (Omega-KA-net) forms a new GMT imaging method that can be applied to high-quality imaging under down-sampling and a low signal to noise ratio (SNR) while saving the imaging time substantially. The experiments of simulation data and measured data demonstrate that the Omega-KA-net is superior to the conventional algorithms in terms of GMT imaging quality and time.

2-D Frequency Autofocus for Squint Spotlight SAR Imaging With Extended Omega-K

In the existing time-domain autofocus algorithms, the azimuth deramping operation will change the azimuth-independent phase into the azimuth-dependent phase, which may greatly reduce the accuracy of autofocus processing in squint spotlight synthetic aperture radar (SAR). In contrast, the frequency-domain autofocus algorithms can avoid this problem because it does not involve the azimuth deramping operation. However, the existing frequency-domain autofocus algorithms are proposed based on the assumption of broadside mode, which cannot be directly applied to the squint mode. Therefore, this article extends the existing frequency-domain autofocus algorithm to the squint mode combined with the extended Omega-K (EOK) algorithm. Furthermore, a space division (SD) algorithm is embedded into the proposed algorithm as preprocessing, which can effectively compensate for the azimuth-dependent motion error. The simulation and real data are processed to verify the effectiveness of the algorithm.

Ultrahigh-Resolution Autofocusing for Squint Airborne SAR Based on Cascaded MD-PGA

Squint ultrahigh-resolution (UHR) synthetic aperture radar (SAR) generally uses the extended Omega-K algorithm (EOK) for range cell migration correction (RCMC). However, the extra range migration and defocusing (ERMD) will be introduced by the EOK when there are motion errors. This problem will be severe as the squint angle increases, which may sharply reduce the signal-to-noise ratio (SNR) and lead to the failure of the existing autofocus methods. In this letter, a UHR autofocus algorithm based on cascaded map-drift (MD)-PGA is proposed. The MD is used for the rough estimation to improve the SNR and the phase gradient algorithm (PGA) is used to accurately estimate the residual error based on a relatively high SNR. The new algorithm combines the advantages of MD and PGA, which can solve the problem of severe defocusing. The processing of airborne real data validates the effectiveness of the proposed algorithm.

A Fast Omega-K Algorithm for Near-Field 3-D Imaging of MIMO Synthetic Aperture Radar Data

Multiple-input-multiple-output synthetic aperture radar (MIMO-SAR) is being studied and used in more and more sensing applications. However, to deal with large-size scanning data without acceleration technology, there is still a certain distance away from real-time operation using the previous state-of-the-art imaging algorithms, which must use complicated interpolation or iteration operations. To conquer this difficulty, a fast imaging algorithm is developed for 3-D near-range imaging on MIMO-SAR. An appropriate expansion is carried out to the coupling phase term, and thus the differential correction for the MIMO data set can be realized with only a range inverse fast Fourier transform (IFFT) and a matched filtering, which are easy to implement. The computational complexity of the algorithm is O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> N ), which is lower than the previous state-of-the-art algorithms. Short-range measurements on a millimeter-waveband MIMO-SAR with different distributed targets demonstrate the performance of the proposed algorithm. Real-time operation is achieved using the algorithm even with a regular CPU.

A Modified Omega-K Algorithm for Near-Field Single-Frequency MIMO-Arc-Array-Based Azimuth Imaging

Inspired by the circular-aperture synthetic aperture radar (Circular-SAR) imaging regime that can provide higher azimuth image resolution, the imaging regime employing the multiple-input-multiple-output (MIMO) arc array is proposed. Moreover, no efficient imaging algorithm is now available for these MIMO arc array setups. This article proposes a modified Omega-K algorithm for near-field azimuth image reconstruction based on the geometry transformation from the single-frequency MIMO arc array to the equivalent MIMO linear array. Note that this geometry transformation relies on the calculation of the phase difference and the definition of the corresponding compensation function. Compared with the single-input-single-output (SISO) arc scan requiring more elements, simulations with good agreement were performed to validate the azimuth image reconstructions of single/multiple targets. Although the computing efficiency of the proposed algorithm for MIMO arc array is lower than that of the traditional Omega-K algorithm for the SISO arc scan, it still has an obvious advantage relative to the traditional backprojection (BP) algorithm that is always taken as the gold standard. Furthermore, three realistic imaging geometries, including the metal strips at different radii, the tilted metal plate, and the human body torso cross section, were simulated to test the fidelity of the proposed reconstruction algorithm. Proof-of-principle experiments were also carried out based on an MIMO arc array with the help of one arc scanner. Finally, both simulation and experimental results validate the effectiveness of the proposed algorithm on azimuth image reconstruction quality.

Extended Omega-k algorithm for synthetic aperture radar imaging in multi-layer medium

Extended Omega-k algorithm for synthetic aperture radar imaging in multi-layer medium

확장 오메가-케이 알고리즘을 기반한 곡선기하에서의 초고해상도 SAR 영상생성 연구

Conventional algorithms based on synthetic aperture radar(SAR) mainly assume that slant-range variations between the radar and target are represented by a hyperbolic-range-equation(HRE) model. However, this HRE model assumption is not valid for spaceborne SAR systems owing to their curved geometry; this significantly degrades performance of the conventional SAR-based algorithms, especially when requiring ultra-high resolution. Therefore, in this paper, we propose a SAR processing chain for curved-orbit geometry using the extended omega-K algorithm(EOKA). In the proposed method, orbit compensation is first applied to mitigate the effect of the HRE error, after which EOKA is performed. Next, azimuth compression is performed based on the polynomial range model, which compensates for the defocusing of SAR images caused by the HRE model error. Through simulations, we verified that the proposed method could provide focused SAR images for curved-orbit and ultra-high resolution cases.

An Imaging Algorithm for Spaceborne High-Squint L-Band SAR Based on Time-Domain Rotation

For spaceborne high-squint L -band synthetic aperture radar (SAR), the long wavelength and high-squint angle result in strong coupling between the range and azimuth directions. In conventional imaging algorithms, linear range walk correction (LRWC) is commonly used to correct linear range cell migration which dominates the coupling. However, LRWC introduces spatial variation in the azimuth direction, limits the depth-of-azimuth-focus (DOAF) and affects the imaging quality. This article constructs a polynomial range model and develops a modified omega-k algorithm to achieve spaceborne high-squint L -band SAR imaging. The key to this algorithm is to rotate the two-dimensional (2-D) data after LRWC in the time domain by a proposed time-rotation (TR) operation that eliminates the DOAF degradation caused by LRWC. The proposed algorithm, which is composed of LRWC, bulk compression, TR, and modified Stolt interpolation, achieves well-focused results at a 1-m resolution and a swath of 4 km × 4 km at a squint angle of 45°.