A Novel Motion Compensation Method Based on Height Term Removing for Spotlight SAR on Circular Trajectories

In view of the vibration and initial phase errors, the azimuth defocusing of the inverse synthetic aperture ladar is seriously affected and the imaging quality is poor. A phase compensation algorithm based on Circular Shifting-Fast Minimum Entropy Algorithm(CS-FMEA) is proposed. Firstly, based on the imaging geometry model of inverse synthetic aperture lidar (ISAL), the influence of phase error on the signal is analyzed, and the expression of phase error is given; Secondly, the phase compensation effect of the fast minimum entropy algorithm is analyzed. The problem of incomplete phase compensation is caused by the residual rotation phase of the algorithm. A method of circular shifting and windowing is proposed to eliminate the influence of rotation on the gate of the distance gate, and the concrete implementation steps of the algorithm are given. Finally, by comparing the simulation results, three indexes of image entropy, contrast and operation efficiency are used to prove that the algorithm can significantly improve the phase error compensation performance.

Cardiac x-ray CT imaging is still challenging due to heart motion, which cannot be ignored even with the current rotation speed of the equipment. In response, many algorithms have been developed to compensate remaining motion artifacts by estimating the motion using projection data or reconstructed images. In these algorithms, accurate motion estimation is critical to the compensated image quality. In addition, since the scan range is directly related to the radiation dose, it is preferable to minimize the scan range in motion estimation. In this paper, the authors propose a novel motion estimation and compensation algorithm using a sinogram with a rotation angle of less than 360°. The algorithm estimates the motion of the whole heart area using two opposite 3D partial angle reconstructed (PAR) images and compensates the motion in the reconstruction process. A CT system scans the thoracic area including the heart over an angular range of 180° + α + β, where α and β denote the detector fan angle and an additional partial angle, respectively. The obtained cone-beam projection data are converted into cone-parallel geometry via row-wise fan-to-parallel rebinning. Two conjugate 3D PAR images, whose center projection angles are separated by 180°, are then reconstructed with an angular range of β, which is considerably smaller than a short scan range of 180° + α. Although these images include limited view angle artifacts that disturb accurate motion estimation, they have considerably better temporal resolution than a short scan image. Hence, after preprocessing these artifacts, the authors estimate a motion model during a half rotation for a whole field of view via nonrigid registration between the images. Finally, motion-compensated image reconstruction is performed at a target phase by incorporating the estimated motion model. The target phase is selected as that corresponding to a view angle that is orthogonal to the center view angles of two conjugate PAR images. To evaluate the proposed algorithm, digital XCAT and physical dynamic cardiac phantom datasets are used. The XCAT phantom datasets were generated with heart rates of 70 and 100 bpm, respectively, by assuming a system rotation time of 300 ms. A physical dynamic cardiac phantom was scanned using a slowly rotating XCT system so that the effective heart rate will be 70 bpm for a system rotation speed of 300 ms. In the XCAT phantom experiment, motion-compensated 3D images obtained from the proposed algorithm show coronary arteries with fewer motion artifacts for all phases. Moreover, object boundaries contaminated by motion are well restored. Even though object positions and boundary shapes are still somewhat different from the ground truth in some cases, the authors see that visibilities of coronary arteries are improved noticeably and motion artifacts are reduced considerably. The physical phantom study also shows that the visual quality of motion-compensated images is greatly improved. The authors propose a novel PAR image-based cardiac motion estimation and compensation algorithm. The algorithm requires an angular scan range of less than 360°. The excellent performance of the proposed algorithm is illustrated by using digital XCAT and physical dynamic cardiac phantom datasets.

Structured light system using a digital video projector is increasingly used for a 3-D shape measurement because of its digital nature. However, the nonlinear gamma of the projector causes the projected fringe patterns to be non-sinusoidal, which results in phase error therefore shape measurement error. Previous work showed that, by using a small look-up-table (LUT), this type of phase error can be reduced significantly for a three-step phase-shifting algorithm. In this research, we prove that this type of phase error compensation method is not limited to a three-step phase-shifting algorithm. It is generic for any phase-shifting algorithm. The phase error compensation algorithm is able to theoretically eliminate the phase error caused by the gamma of the projector completely. It is based on our finding that in phase domain, the phase error due to the projector's gamma is preserved for arbitrary object's surface reflectivity under arbitrary ambient light condition. The phase error can be pre-calibrated and stored into a LUT for phase error reduction. In this research, we captured a set of fringe images of a uniform flat surface board for such a calibration. The phase error of the flat board is analyzed and stored in a LUT for phase error compensation. Our experimental results show that by using this method, the measurement error can be reduced by at least 13 times for any phase-shifting algorithm.

One method to detect obstacles from a vehicle moving on a planar road surface is the analysis of motion-compensated difference images. In this contribution, a motion compensation algorithm is presented, which computes the required image-warping parameters from an estimate of the relative motion between camera and ground plane. The proposed algorithm estimates the warping parameters from displacements at image corners and image edges. It exploits the estimated confidence of the displacements to cope robustly with outliers. Knowledge about camera calibration, measuremts from odometry, and the previous estimate are used for motion prediction and to stabilize the estimation process when there is not enough information available in the measured image displacements. The motion compensation algorithm has been integrated with modules for obstacle detection and lane tracking. This system has been integrated in experimental vehicles and runs in real time with an overall cycle of 12.5 Hz on low-cost standard hardware.

In unmanned aerial vehicle (UAV) synthetic aperture radar (SAR), step-frequency mode is usually used due to the limitation of size and weight. Due to the small size and weight, the trajectory deviation is so serious that the motion compensation becomes very complex. In order to estimate and compensate the motion error in UAV SAR, a two-step motion compensation approach is proposed in this paper. Firstly, the global positioning system (GPS) and inertial navigation system (INS) data is used for the coarse compensation to eliminate the major motion error. Secondly, fine phase error compensation based on raw SAR data is processed to circumvent the residual phase error. The fine phase error is estimated by weighted phase gradient autofocus (WPGA) in each sub-pulse of step-frequency mode. Then the weight least square (WLS) method is used to obtain the final focusing phase from the estimated phase of sub-pulse. Real data experiments show that the proposed method is suitable for UAV SAR motion compensation.

Airborne synthetic aperture radar (SAR) system is an essential tool for modern remote sensing applications. The aircraft is easily affected by the atmospheric turbulence, leading to deviations from the ideal track. To enable high-resolution imagery, a navigation system is usually mounted on the aircraft. Due to the limitation of the navigation system's accuracy, motion errors estimated from the SAR raw data are needed. In this paper, a novel motion compensation algorithm, which is based on the instrumental variables (IV) method, is proposed. We call this IV-based algorithm the IVA algorithm. In this algorithm, double-derivative motion errors are estimated without modeling the random disturbances to be a zero-mean Gaussian distribution and to be created from mutually independent noise, which makes it more robust and accurate in focusing SAR images. Before the motion error estimation, a Savitzky–Golay filter is performed to reduce the phase estimation errors, in which the phase is obtained by the phase gradient autofocus algorithm. Finally, the estimated motion errors are used to compensate the received signal with the range-dependent model. The IVA algorithm is validated by using real airborne SAR data, and experimental results show that the proposed algorithm achieve an excellent performance in airborne SAR systems.

This paper proposes a novel motion compensation algorithm for wide beam Synthetic Aperture Radar (SAR) based on frequency division. It applies motion compensation in time domain and corrects both low- and high- frequency motion errors. The rationale and procedure of this algorithm are introduced in detail. Point scatterers of a P-band airborne SAR with different motion errors are tested to validate this algorithm. Compared with traditional narrow beam motion compensation and available wide beam compensation, the proposed algorithm has better performance.

Aperture-dependent motion compensation is important for wide beam Synthetic Aperture Radar (SAR) data processing. This paper studies a wide beam motion compensation algorithm based on frequency division. It takes blocks along azimuth dimension in frequency domain and applies angle-variant motion compensation in time domain. With this frequency division based motion compensation approach, the effects of aperture-dependent residual phase errors are corrected precisely. The rationale and procedure of this algorithm are introduced in detail. Point targets and images of a P-band airborne SAR with motion errors are simulated to validate this algorithm. Compared with the wide beam motion compensation algorithms based on time division, the proposed algorithm has better performance, especially in terms of high-frequency motion errors.

Real-time video image processing requires video compression techniques. Efficient Motion Estimation (ME) and Motion Compensation (MC) algorithms and their successful hardware implementation are the key to video compression. Work on developing and implementing efficient ME and MC algorithms for multi-camera systems is ongoing. The low power consumption yet high speed of Heterogeneous Reconfigurable Devices such as Field Programmable Gate Arrays (FPGA) can be suitable for implementation of real-time optic flow computation using multi-camera systems. This paper focuses on a search into the current state-of-the-art for multi-camera motion tracking. It has been found the tracking systems mainly focused on people and vehicle tracking in both indoor and outdoor conditions, tracking under occlusion, tracking for surveillance, single and multi-view tracking, etc. The review search also found use of multi-camera tracking in the medical sector, such as multi-camera tracking systems for respiratory motion tracking. Research on this field has not been explored much and this holds possibilities for further work.

This letter presents a comparison between three Fourier-based motion compensation (MoCo) algorithms for airborne synthetic aperture radar (SAR) systems. These algorithms circumvent the limitations of conventional MoCo, namely the assumption of a reference height and the beam-center approximation. All these approaches rely on the inherent time-frequency relation in SAR systems but exploit it differently, with the consequent differences in accuracy and computational burden. After a brief overview of the three approaches, the performance of each algorithm is analyzed with respect to azimuthal topography accommodation, angle accommodation, and maximum frequency of track deviations with which the algorithm can cope. Also, an analysis on the computational complexity is presented. Quantitative results are shown using real data acquired by the Experimental SAR system of the German Aerospace Center (DLR).

Coded-aperture antenna plays an important role in terahertz coded-aperture imaging radar system. However, the performance of a system is inevitably affected by the phase errors introduced by the coded-aperture antenna elements. In this paper, we propose a phase error compensation method by deducing a formula to compute all element phase errors accurately. According to the formula, the phase errors can be calibrated by using a calibrator and can be used to compensate the imaging model of the system. Numerical simulations demonstrate that the proposed method can effectively improve the imaging quality when the elemental phase error exceeds 10 ∘ .

To obtain a high-resolution and wide-swath image, the azimuth multichannel technique has been widely used in synthetic aperture radar (SAR) systems to overcome the contradiction between the wide swath and high pulse repetition frequency. For a high image quality, channel mismatch correction is an essential step in the multichannel SAR data imaging. However, in the case of airborne multichannel SAR, motion errors will severely degrade the performance of channel mismatch correction. To deal with this problem, this article proposes an improved airborne multichannel SAR imaging method with motion compensation, and range-variant channel mismatch correction. First, motion errors are compensated based on resampling and phase compensation. Then, the time-delay and constant gain-phase errors between channels are estimated and corrected, followed by the range-variant phase error correction based on a novel range-down-sampling method, which reduces the influence of motion errors on the channel mismatch correction significantly. Finally, simulated and real data processing results are used to demonstrate the effectiveness of the proposed method.

Aiming at the higher bit-rate occupation of motion vector encoding and more time load of full-searching strategies, a multi-resolution motion estimation and compensation algorithm based on adjacent prediction of frame difference was proposed. Differential motion detection was employed to image sequences and proper threshold was adopted to identify the connected region. Then the motion region was extracted to carry out motion estimation and motion compensation on it. The experiment results show that the encoding efficiency of motion vector is promoted, the complexity of motion estimation is reduced and the quality of the reconstruction image at the same bit-rate as Multi-Resolution Motion Estimation (MRME) is improved.

Until today, several software-based approaches to increase the temporal resolution in cardiac computed tomography by estimating motion vector fields (MVFs) have been developed. Thereunder, the majority are motion compensation algorithms, which estimate the MVFs employing a three-dimensional registration routine working on reconstructions of multiple cardiac phases.^{2, 6, 7, 12}We present an algorithm that requires nothing more than the data needed for a short scan reconstruction for motion estimation and motion-compensated reconstruction, which both are based on the reconstruction of volumes from a limited angular range.^{2, 3, 7, 8} Those partial angle reconstructions are centered at different time points during the short scan and have a temporal resolution of about 10ms each. The MVFs are estimated by a constrained cost function optimization routine employing a motion artifact measuring cost function. During optimization, the MVFs are applied directly by warping the partial angle reconstructions, and the motion compensation is established by simply adding the shifted images. In order to enforce smooth vector fields and keep the number of parameters low, the motion is modeled by a low degree polynomial. Furthermore, to find a good estimation of the MVFs even in phases with rapid cardiac motion, the constrained optimization is re-initialized multiple times. The algorithm is validated with the help of a simulation study and applied to patient data, where motion- compensated reconstructions are performed in various cardiac phases. We show that the image quality can be improved, also in more rapid cardiac phases due to re-initialization of the optimization routine.

Synthetic transmit aperture (STA) has been widely investigated in ultrasound system recently with characteristics of high frame rate and low hardware cost. Since the high-resolution image (HRI) of STA is formed by summation of low-resolution images (LRIs), it is susceptible to inter-firing motions. In this paper, we propose a low-complexity global motion compensation algorithm. We use the common region of interest (ROIcom) between different transmissions of STA imaging to beamform backward and forward beam vectors. Then, the magnitude and direction of motion can be evaluated by cross-correlations between specific beam vectors in STA imaging. Compared with the uncompensated image in two-dimentional (2D) motion environment, the proposed motion compensation algorithm can improve the contrast ratio (CR) and contrast-to-noise ratio (CNR) by 13.73 and 2.04 dB, respectively. Also, the proposed algorithm improves the CR and CNR about 7.84 and 1.36 dB comparing with the reference work, respectively. In the Field II breath model, the proposed method also improves the CR and CNR about 6.65 and 1.04 dB than the reference method, respectively. Moreover, we propose a low-complexity delay generator in the architecture design to further reduce the computational complexity of the whole beamforming system. Finally, we verify the proposed low-complexity motion compensation beamforming engine by using the VLSI implementation with CMOS 90 nm technology. In the post-layout result, the core size is 2.39 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at 125 MHz operating frequency and the frame rate of the beamforming system is 42.23 frames per second.