Backprojection Image Research Articles

A HRWS SAR Motion Compensation Method with Multichannel Phase Correction

The multichannel synthetic aperture radar (SAR) possesses the capability to acquire high-resolution, wide-swath SAR imagery, which has great potential for application. However, similar to traditional single-channel SAR systems, it suffers from imaging quality degradation due to motion errors. Many motion compensation algorithms have been used to improve the quality of single-channel SAR images, while fewer studies have been conducted on multichannel SAR motion compensation methods. The sub-image motion compensation method utilizes the single channel motion errors to perform multichannel motion errors compensation, considering that multiple channels have the same phase errors. To improve the quality of multichannel SAR imaging when multiple channel motion errors are inconsistent, this paper proposes a motion compensation method with multichannel phase correction for HRWS SAR. First, the method derives the phase errors estimation model via maximum sharpness to simultaneously estimate multichannel phase. Then, it compensates for the motion errors of all channels during backprojection imaging. The inconsistent motion errors of multiple channels can be compensated by estimating the phase errors of all channels, improving the image quality. The channel phase errors can be corrected while compensating for the motion errors. Moreover, the experimental results of point targets and complex scenes validate the effectiveness of the proposed method.

Rotor unmanned aerial vehicle localization in the building sheltered area based on millimetre‐wave frequency‐modulated continuous wave radar

AbstractRotor unmanned aerial vehicles (UAVs) play an important role in both military and civilian fields nowadays. The safety risks associated with the UAVs increase the urgent need for detecting UAVs in urban environments as well. Moreover, UAVs are easily located in the non‐line‐of‐sight (NLOS) building sheltered area relative to the radar, making it very challenging to detect and localise. A novel algorithm for localising the rotor UAV in the common L‐shaped street building sheltered area is proposed. First, the authors establish a multipath signal model for a rotor UAV hovering over an L‐shaped street scene, leveraging the frequency‐modulated continuous wave signal. Then, the multipath information of the UAV is extracted by identifying the rotating periodicity of the blade embedded in the time‐frequency spectrum of the received signal. The back projection imaging is then conducted on the UAV‐related multipath. After extracting multipath ghosts in the image, the street area, where the UAV locates, can be determined, and the UAV is further localised using the path reflection characteristics of this area. Simulations and practical experiments based on millimetre waves indicate that the proposed method can enable high‐accuracy estimation of rotor UAV in the NLOS building sheltered area.

The effects of back-projection variants in BPF-like TOF PET reconstruction using CNN filtration - Based on simulated and clinical brain data.

The back-projection strategies such as confidence weighting (CW) and most likely annihilation position (MLAP) have been adopted into back-projection-and-filtering-like (BPF-like) deep reconstruction model and shown great potential on fast and accurate PET reconstruction. Although the two methods degenerate to an identical model at the time resolution of 0ps, they represent two distinct approaches at the realistic time resolutions of current commercial systems. There is a lack of a systematic and fair assessment on these differences. This work aims to analyze the impact of back-projection variants on CNN-based PET image reconstruction to find the most effective back-projection model, and ultimately contribute to accurate PET reconstruction. Different back-projection strategies (CW and MLAP) and different angular view processing methods (view-summed and view-grouped) were considered, leading to the comparison of four back-projection variants integrated with the same CNN filtration model. Meanwhile, we investigated two strategies of physical effect compensation, either introducing pre-corrected data as the input or adding a channel of attenuation map to the CNN model. After training models separately on Monte-Carlo-simulated BrainWeb phantoms with full dose (events=3×107), we tested them on both simulated phantoms and clinical brain scans with two dosage levels. For the performance assessment, peak signal-to-noise ratio (PSNR) and root mean square error (RMSE) were used to evaluate the pixel-wise error, structural similarity index (SSIM) to evaluate the structural similarity, and contrast recovery coefficient (CRC) in manually selected ROI to compare the region recovery. Compared to two MLAP-based histo-image reconstruction models, two CW-based back-projected image methods produced clearer, sharper, and more detailed images, from both simulated and clinical data. For angular view processing methods, view-grouped histo-image improved image quality, while view-grouped cwbp-image showed no advantage except for contrast recovery. Quantitative analysis on simulated data demonstrated that the view-summed cwbp-image model achieved the best PSNR, RMSE, SSIM, while the 8-view cwbp-image model achieved the best CRC in lesions and the white matter. Additionally, the multi-channel input model including the back-projection image and attenuation map was proved to be the most efficient and simplest method for compensating for physical effects for brain data. Applying Gaussian blur to the histo-image yielded images with limited improvement. All above results hold for both the half-dose and the full-dose cases. For brain imaging, the evaluation based on metrics PSNR, RMSE, SSIM, and CRC indicates that the view-summed CW-based back-projection variant is the most effective input for the BPF-like reconstruction model using CNN filtration, which can involve the attenuation map through an additional channel to effectively compensate for physical effects.

Trajectory Deviation Estimation Method for UAV-Borne Through-Wall Radar

Mini–unmanned aerial vehicles (mini-UAVs) are emerging as a promising platform for through-wall radar to sense the enclosed space in cities, especially high-rise buildings, due to their excellent maneuverability. However, due to unavoidable environmental interference such as airflow, mini-UAVs are prone to trajectory deviation thus degrading their sensing accuracy. Most of the existing approaches model the impact of trajectory deviation into a polynomial phase error on the received signal, which cannot fit the space-variant motion error well. Moreover, the large trajectory deviations of UAVs introduce the unavoidable envelope error. This article proposes an autofocusing algorithm based on the back projection (BP) image, which directly estimates the trajectory deviations between the actual and measured track. Thus, the problem of the 2D space variability of the motion error can be circumvented. The proposed method mainly consists of two steps. First, we estimate the trajectory deviation in the line-of-sight (LOS) direction by exploring the underlying linear property of the wall embedded in the BP imaging result. Then, the estimated trajectory deviation in the LOS direction is compensated for to obtain an updated BP image, followed by a Particle Swarm Optimization (PSO) approach to estimate the trajectory deviation along the track through focusing targets behind the wall. Simulations and practical experiments show that the proposed algorithm can accurately estimate the serious trajectory deviations larger than the range resolution, improving the sensing robustness of UAV-borne through-wall radar greatly.

Point spread function modeling for photoacoustic tomography - I: three-dimensional detection geometries.

Photoacoustic computed tomography (PACT) has been under intensive investigation as a promising noninvasive biomedical imaging modality. Various acoustic detector arrays have been developed to achieve enhanced imaging performance. In this paper, we study the effect of the detection geometry on image quality through point spread function (PSF) modeling based on back-projection image reconstruction. Three commonly-used three-dimensional detection geometries, namely, spherical, cylindrical, and planar detector arrays, are investigated. The effect of detector bandwidth and aperture on PSF in these detection geometries is also studied. This work provides a performance evaluation tool for acoustic detector arrays used in PACT and can be helpful in the design and selection of detector arrays in practical imaging applications.

Moving Target Tracking Method Based on Improved Camshift

<p>Aiming at the problem that target occlusion and other disturbances in complex background will reduce the tracking accuracy of moving target, and even lead to tracking failure, this paper proposes a moving target tracking algorithm based on the improved Camshift algorithm. Firstly, Gaussian background is used to model the foreground image to improve the backprojection image, and then the interference of backprojection is removed to improve the tracking effect in complex background conditions. Secondly, Kalman filtering is utilized to predict the trajectory, which further improves the tracking accuracy of Camshift algorithm in occlusion condition. A lot of experiments are processed, and the results show that the proposed algorithm could effectively improve the tracking accuracy and meet the real-time requirements.</p> <p> </p>

Deep Learning-Based Single-View Fluorescence Dose Reconstruction for 3D Dosimetry

3D dose distribution measurement is crucial for precise radiotherapy. Radiation-excited fluorescence imaging has potential for the 3D dosimetry with high spatial resolution, but multiple fluorescence images from different view-angles are required for analytical reconstruction techniques. Furthermore, the imaging data are contaminated by anisotropic Cherenkov light emission and statistical noise. This project aims to establish a novel deep learning-based model to predict 3D dose distributions from a single-view 2D fluorescence image while simultaneously removing the adverse effects of Cherenkov signals and other noises. A total of 124 single-aperture static photon beams were delivered to an acrylic tank containing 1 g/L quinine hemisulfate water solution with varying aperture shapes and collimator angle. The emitted optical signals were detected by a low-cost CMOS camera for 20 seconds, and image pre-processing was performed to obtain input 2D fluorescence images with 0.3 × 0.3 mm spatial resolution. 3D back-projected dose distribution images were also calculated from the input fluorescence images. Ground-truth of 3D dose distributions and 2D field map images were obtained from a clinical treatment planning system with 1.4 × 1.4 × 1.4 mm spatial resolution. The proposed deep learning-based dose reconstruction method involved 3 steps. First, 2D fluence map images at the bottom plane of the tank were predicted from the fluorescence images by using a customized convolutional neural network (CNN). Second, the predicted fluence map images were transformed into the 2D field map images on the isocenter plane by applying perspective transformation. Finally, 2D dose distributions at a given radiological depth were calculated by using the predicted field map images, the back-projected dose distribution images, and the radiological depth value as inputs of a shallow CNN. Both CNN models were trained separately, and the 3D dose distributions were predicted by concatenating the output 2D dose distributions at various radiological depths. The proposed CNN model yielded accurate 2D field map images. Averaged Dice similarity coefficient and mean absolute error of the field maps in the test data was 92.0% ± 4.6% and 0.0132 ± 0.0113, respectively. Moreover, our deep learning-based approach was able to predict accurate 3D dose distributions from the 2D fluorescence images. Mean squared error and averaged 3D gamma passing ratio (3%/3mm) were 9.55 mGy ± 6.8 mGy and 86.3% ± 9.86%, respectively. Theproposed deep learning-based method calculated accurate 3D dose distributions from a single-view 2D fluorescence image. Since this technique require only a single CMOS camera image and fluorescent material, it can be readily used for any external radiotherapy modalities, including SRS/SBRT with small fields. This method is useful for acquiring 3D dose distribution data for precise dose verification within a few seconds.

Asymmetric Bilateral Rupture of the 2022 Ms 6.8 Luding Earthquake on a Continental Transform Fault, Tibetan Border, China

Abstract The Xianshuihe (XSH) fault on the eastern boundary of the Tibetan plateau is one of the most active faults in the world. However, the Moxi fault, the southernmost segment of the XSH fault, remained seismically quiescent for over 230 yr, with a large slip rate and high locking degree. Thus, this region is considered to be a seismic gap capable of hosting earthquakes of Mw 7.0 or greater. In September 2022, the Ms 6.8 Luding earthquake occurred on the Moxi fault, resulting in destructive landslide damage, with 93 people dead and 25 missing. Using regional and global seismic recordings, we integrate the multiple-point-source analysis, finite-fault inversions, and backprojection imaging to investigate in detail the rupture process associated with the 2022 Luding, China, earthquake. Our results show that this event is characterized by an asymmetric bilateral rupture with three episodes: (1) an initial bilateral rupture propagation mainly toward north-northwest; (2) major rupture propagating toward south-southeast and up-dip direction; (3) south-southeast-rupture propagation speed accelerates to ∼2 km/s. Over 70% of the seismic moment is released at shallow depths <12 km thus explaining significant damaging effects. Furthermore, the seismic potential of the remaining locked portions of the XSH and Anninghe faults is still high and positive increases of the Coulomb stress on these faults due to the Luding earthquake might bring them closer to future failure.

Locating volcanic tremor using azimuth coherence of cross-correlation

Accurate localization of volcanic tremors can provide important information about volcanic activities. However, the seismic waveform of volcanic tremor is complicated, resulting in that its location cannot be accurately determined from traditional traveltime inversion methods due to the unidentifiable first arrivals. The cross-correlation-based back-projection method, which stacked the back-projected spatial images utilizing the cross-correlation data from different station pairs, is considered as one of the most effective waveform stacking location methods for the volcanic tremor. In this method, the obtained coherence from different station pairs can improve the signal-to-noise ratio of projected energy distribution, and then constrain the potential source location. Nevertheless, not all back-projected images of station pairs are helpful to enhance the positioning effect in practice because the resolution of the energy peak in the back-projection method is affected by the selection of used station pairs. In this study, we optimized the back-projection method by establishing some criteria for the selection of the station pairs, including the distance between two stations in each pair, and the calculated azimuth angle, the cover area, and the central location between each two of all station pairs. In addition, the phase information in cross-correlation data has been also used in our method to limit the energy divergence in the resulting map. Taking the Katla volcano as a real example, we demonstrate that the proposed second-order azimuth coherent location method can increase the accuracy of locating volcanic tremors compared to the traditional methods, resulting in an improvement of approximately 70 % in location resolution.

Strategies to improve the range verification of stochastic origin ensembles for low-count prompt gamma imaging

The stochastic origin ensembles method with resolution recovery (SOE-RR) has been proposed to reconstruct proton-induced prompt gammas (PGs), and the reconstructed PG image was used for range verification. However, due to low detection efficiency, the number of valid events is low. Such a low-count condition can degrade the accuracy of the SOE-RR method for proton range verification. In this study, we proposed two strategies to improve the reconstruction of the SOE-RR algorithm for low-count PG imaging. We also studied the number of iterations and repetitions required to achieve reliable range verification. We simulated a proton beam (108 protons) irradiated on a water phantom and used a two-layer Compton camera to detect 4.44-MeV PGs. Our simulated results show that combining the SOE-RR algorithm with restricted volume (SOE-RR-RV) can reduce the error of the estimation of the Bragg peak position from 5.0 mm to 2.5 mm. We also found that the SOE-RR-RV algorithm initialized using a back-projection image could improve the convergence rate while maintaining accurate range verification. Finally, we observed that the improved SOE-RR algorithm set for 60,000 iterations and 25 repetitions could provide reliable PG images. Based on the proposed reconstruction strategies, the SOE-RR algorithm has the potential to achieve a positioning error of 2.5 mm for low-count PG imaging.

Noise power spectrum properties of deep learning–based reconstruction and iterative reconstruction algorithms: Phantom and clinical study

PurposeTo compare the noise power spectrum (NPS) properties and perform a qualitative analysis of hybrid iterative reconstruction (IR), model-based IR (MBIR), and deep learning–based reconstruction (DLR) at a similar noise level in clinical study and compare these outcomes with those in phantom study. MethodsA Catphan phantom with an external body ring was used in the phantom study. In the clinical study, computed tomography (CT) examination data of 34 patients were reviewed. NPS was calculated from DLR, hybrid IR, and MBIR images. The noise magnitude ratio (NMR) and the central frequency ratio (CFR) were calculated from DLR, hybrid IR, and MBIR images relative to filtered back-projection images using NPS. Clinical images were independently reviewed by two radiologists. ResultsIn the phantom study, DLR with a mild level had a similar noise level as hybrid IR and MBIR with strong levels. In the clinical study, DLR with a mild level had a similar noise level as hybrid IR with standard and MBIR with strong levels. The NMR and CFR were 0.40 and 0.76 for DLR, 0.42 and 0.55 for hybrid IR, and 0.48 and 0.62 for MBIR. The visual inspection of the clinical DLR image was superior to that of the hybrid IR and MBIR images. ConclusionDeep learning–based reconstruction improves overall image quality with substantial noise reduction while maintaining image noise texture compared with the CT reconstruction techniques.

Precursors for synthetic aperture radar

In this paper we study waveform design for synthetic-aperture radar (SAR) imaging through dispersive media. Under the assumptions of scalar wave propagation through a causal dielectric medium and single-scattering from an isotropic point scatterer, we use asymptotic analysis to derive the asymptotic approximation to the scattered electric field. From this asymptotic approximation, we define a sensing precursor that we propose for the transmit waveform for SAR imaging through dispersive material. We compare our sensing precursor with previously defined optimal waveforms (Varslot et al 2011 SIAM J. Appl. Math. 71 1780–800) in terms of both propagation and scattering capabilities, as well as imaging performance. With the filtered back-projection imaging algorithm that we use, we find that for high levels of signal-to-noise ratio (SNR), the optimal waveforms contain higher frequencies and thus produce better images. For low levels of SNR, the transmitted optimal waveforms and the sensing precursors are similar, thus giving comparable images.

Video SAR Moving Target Shadow Detection Based on Intensity Information and Neighborhood Similarity

Video Synthetic Aperture Radar (SAR) has shown great potential in moving target detection and tracking. At present, most of the existing detection methods focus on the intensity information of the moving target shadow. According to the mechanism of shadow formation, some shadows of moving targets present low contrast, and their boundaries are blurred. Additionally, some objects with low reflectivity show similar features with them. These cause the performance of these methods to degrade. To solve this problem, this paper proposes a new moving target shadow detection method, which consists of background modeling and shadow detection based on intensity information and neighborhood similarity (BIIANS). Firstly, in order to improve the efficiency of image sequence generation, a fast method based on the Back-projection imaging algorithm (f-BP) is proposed. Secondly, due to the low-rank characteristics of stationary objects and the sparsity characteristics of moving target shadows presented in the image sequence, this paper introduces the low-rank sparse decomposition (LRSD) method to perform background modeling for obtaining better background (static objects) and foreground (moving targets) images. Because the shadows of moving targets appear in the same position in the original and the corresponding foreground images, the similarity between them is high and independent of their intensity. Therefore, using the BIIANS method can obtain better shadow detection results. Real W-band data are used to verify the proposed method. The experimental results reveal that the proposed method performs better than the classical methods in suppressing false alarms, missing alarms, and improving integrity.

QuantifyingP-wave secondary microseisms events: a comparison of observed and modelled backprojection

SUMMARYSecondary microseisms are caused by nonlinear interactions between ocean waves of approximately equal wavelengths and opposite propagation directions. This seismic forcing is evaluated using ocean sea-state hindcast data and further modulated by the bathymetric effect. The numerical ocean model provides a global activity representation of the secondary microseisms, from which we isolate major events. We backprojected teleseismic P-wave propagation into the Earth's mantle to validate these events as effective seismic sources. The ocean model provides spectral amplitude information for modelling microseisms generated seismic wavefield. A comparison of the backprojection for P and PP phases from observed and synthetic microseisms forcing indicates high reliability in the ocean model, at least for major sources. A combination of P and PP phases detected across a global network of stations enables global ocean coverage. We improve backprojection images even further by introducing a two-step stacking for the P phase to address the problem of unbalanced station distribution. Thresholds of microseisms events forces valuable for seismic imaging are determined by comparing backprojections and ocean models for the years 2015 and 2020. Finally, we extracted a catalogue of microseisms events every 3-hr from 1994 to 2020 from the ocean hindcast data set. This catalogue is an intriguing resource for future applications of interferometric imaging at large scale.

Comparison of Deep-Learning Image Reconstruction With Hybrid Iterative Reconstruction for Evaluating Lung Nodules With High-Resolution Computed Tomography.

This study aimed to investigate the impact of deep-learning reconstruction (DLR) on the detailed evaluation of solitary lung nodule using high-resolution computed tomography (HRCT) compared with hybrid iterative reconstruction (hybrid IR). This retrospective study was approved by our institutional review board and included 68 consecutive patients (mean ± SD age, 70.1 ± 12.0 years; 37 men and 31 women) who underwent computed tomography between November 2021 and February 2022. High-resolution computed tomography images with a targeted field of view of the unilateral lung were reconstructed using filtered back projection, hybrid IR, and DLR, which is commercially available. Objective image noise was measured by placing the regions of interest on the skeletal muscle and recording the SD of the computed tomography attenuation. Subjective image analyses were performed by 2 blinded radiologists taking into consideration the subjective noise, artifacts, depictions of small structures and nodule rims, and the overall image quality. In subjective analyses, filtered back projection images were used as controls. Data were compared between DLR and hybrid IR using the paired t test and Wilcoxon signed-rank sum test. Objective image noise in DLR (32.7 ± 4.2) was significantly reduced compared with hybrid IR (35.3 ± 4.4) (P < 0.0001). According to both readers, significant improvements in subjective image noise, artifacts, depictions of small structures and nodule rims, and overall image quality were observed in images derived from DLR compared with those from hybrid IR (P < 0.0001 for all). Deep-learning reconstruction provides a better high-resolution computed tomography image with improved quality compared with hybrid IR.

T-Matrix Backprojection Imaging for Scalar and Vector Electromagnetic Waves

Expressions for the ideal free-space backprojected image of an object with known transition matrix (T-matrix) are derived for scalar and vector electromagnetic waves in bistatic and monostatic geometries. Discrete backprojection sums are extended to continuous integrals over source/receiver spheres. Images are formed without the need to generate or process scattered field data. The final expressions only depend on regular wave functions in the frame of the object and the object T-matrix. The formulation is validated numerically using the aggregate T-matrix solution for a collection of acoustic and dielectric spheres. Applications include assessment and validation of free-space focusing and T-matrix scattering solutions.

Back-Projection Imaging for Synthetic Aperture Radar with Topography Occlusion

When synthetic aperture radar (SAR) is conducting remote sensing or terrain mapping, its radar beam is inevitably occluded by the variations in the under-test topography. Although back-projection algorithm (BPA) can theoretically directly solve the imaging problems of topography variations that most current SAR imaging algorithms cannot handle, these BPAs only solve the phase focusing of SAR echo signal, and do not consider the mismatch of SAR imaging results caused by topography occlusion. To solve the mis-imaging issue of the occluded area generated by BPA under the case of topography variation, a topography-based BPA (Topo-BPA) is proposed in this paper. Firstly, a new beam occlusion judgment algorithm based on spherical wave assumption is proposed, and its core is depression angle interpolation and depression angle updating. Then, the proposed Topo-BPA embeds the proposed beam occlusion judgment algorithm before the classical BPA, which not only did not reduce the focus depth of BPA, but improved the imaging accuracy of classical BPA. Finally, numerical experiments have demonstrated the superiority of the Topo-BPA’s performance in comparison with classical BPA.

An Image-Domain Signal Model for Azimuth Multichannel Reconstruction and Its Applications

High-resolution wide-swath (HRWS) synthetic aperture radar (SAR) may benefit from reconstructing signal in image domain, for taking local characteristics of the scene into account. An image-domain signal model for HRWS SAR to reconstruct non-ambiguous image is presented in this paper. This model makes the idea of controlling the regional reconstruction performance and taking the advantage of nonuniform scatter distribution possible. Resolution is also preserved perfectly by the proposed model despite of whatever tradeoff is made between azimuth-ambiguity-to-signal-ratio (AASR) and signal-to-noise-ratio (SNR). The model is derived on back projection (BP) image and can deal with different squint angles and beam steering strategies thanks to BP algorithm. Although the reconstruction is done pixel by pixel, computational burden, which depends on beam steering and the specific constraints in reconstruction, may not severely increase. Two methods for Spotlight SAR and two methods for Stripmap SAR are also presented based on the proposed model to verify the model and demonstrate the potential of it. Simulations on both point target and extended target with different squint angles are carried out to verify the proposed methods, which also verify the proposed model indirectly.

A graphical user interface (GUI) for model-based radiation-induced acoustic computed tomography

Radiation-induced acoustic computed tomography (RACT) is an evolving biomedical imaging modality that aims to reconstruct the radiation energy deposition in tissues. Traditional back-projection (BP) reconstructions carry noisy and limited-view artifacts. Model-based algorithms have been demonstrated to overcome the drawbacks of BPs. However, model-based algorithms are relatively more complex to develop and computationally demanding. Furthermore, while a plethora of novel algorithms has been developed over the past decade, most of these algorithms are either not accessible, readily available, or hard to implement for researchers who are not well versed in programming. We developed a user-friendly MATLAB-based graphical user interface (GUI; RACT2D) that facilitates back-projection and model-based image reconstructions for two-dimensional RACT problems. We included numerical and experimental X-ray-induced acoustic datasets to demonstrate the capabilities of the GUI. The developed algorithms support parallel computing for evaluating reconstructions using the cores of the computer, thus further accelerating the reconstruction speed. We also share the MATLAB-based codes for evaluating RACT reconstructions, which users with MATLAB programming expertise can further modify to suit their needs. The shared GUI and codes can be of interest to researchers across the globe and assist them in efficient evaluation of improved RACT reconstructions.

NLOS Positioning for Building Layout and Target Based on Association and Hypothesis Method

Localization of non-line-of-sight (NLOS) targets in the complex urban environment have attracted significant attention in recent years. However, the requirement for precise prior information about the environment is idealistic. It is challenging to know the environmental information in the blind area of vision in advance of practical applications. This paper proposes a joint estimation algorithm for building layout and target position in the L-shaped scene without any prior information. Specifically, a round-trip multipath propagation model is first developed for the cases of diffraction and multiple reflections. Then, the received echo signal is preprocessed with moving target identification (MTI), back-projection (BP) imaging, and image segmentation. In addition, the target points, which are screened by geometric association, are further matched and estimated by the multipath ghost’s hypothesis method, thus realizing the joint perceptual estimation of the building layout and the target position. Finally, electromagnetic (EM) simulations and experimental measurements are used to validate the effectiveness of the proposed algorithm.