Phase Unwrapping Technique Research Articles

A low-complexity ISAC method for LFM-PSK signals using de-chirping and ISAC phase unwrapping techniques

Integrated Sensing and Communication (ISAC) has the potential to revolutionize wireless technology in areas such as autonomous vehicles, the Internet of Things, and unmanned aerial vehicle navigation technology. Nonetheless, conventional processing methods for Linear Frequency Modulation-Phase Shift Keying (LFM-PSK) signals predominantly depend on matched filtering, leading to high sampling rates and computational complexity. In response to these challenges, our research proposes a method to process LFM-PSK signals, which enables the use of de-chirping techniques. Applying the proposed ISAC unwrapping technique makes it possible to selectively recover the phase of the de-chirped LFM-PSK signal. Subsequently, the distance can be calculated by analyzing the slope of the recovered phase. Moreover, by adjusting the threshold in the ISAC unwrapping technique, communication information can be extracted by detecting phase hops associated with PSK. This method offers an attractive alternative to traditional methods such as matched filtering and coherent demodulation techniques. We derive the Cramér-Rao lower bound (CRLB) for ranging. Theoretical analysis and simulation indicate that our method effectively reduces the required sampling rate and provides higher-ranging performance than the matched filtering technique in radar sensing. In high signal-to-noise ratio scenarios, our proposed method delivers a ranging performance close to that of CRLB. Regarding communication, our method has the advantage of lower synchronization requirements, making it more feasible for practical engineering applications than the conventional coherent demodulation method. Furthermore, it also necessitates lower computational resources compared to matched filtering techniques. Importantly, our method allows high device sharing, promoting cost-effective ISAC implementation.

An On-Site InSAR Terrain Imaging Method with Unmanned Aerial Vehicles.

An on-site InSAR imaging method carried out with unmanned aerial vehicles (UAVs) is proposed to monitor terrain changes with high spatial resolution, short revisit time, and high flexibility. To survey and explore a specific area of interest in real time, a combination of a least-square phase unwrapping technique and a mean filter for removing speckles is effective in reconstructing the terrain profile. The proposed method is validated by simulations on three scenarios scaled down from the high-resolution digital elevation models of the US geological survey (USGS) 3D elevation program (3DEP) datasets. The efficacy of the proposed method and the efficiency in CPU time are validated by comparing with several state-of-the-art techniques.

Phase denoising and unwrapping method for moiré fringes based on multiresolution analysis

Phase unwrapping for moiré fringes plays a crucial role in moiré tomography, and the precision of its outcomes deeply influences the detection results concerning high-temperature complex flow fields. In this paper, a phase denoising and unwrapping technique grounded in multiresolution analysis (MRA) is presented, and it is effectively applied to extract phase information from moiré fringes for propane-air flame and argon arc plasma flow fields. Firstly, the wrapped phase undergoes a wavelet packet decomposition for overall denoising. Subsequently, MRA is conducted to refine the denoising process and unwrap phase, involving layered wavelet packet decomposition and iterative unwrapping on different levels of approximate components. Following the hierarchical structure of MRA, the results from different levels are systematically combined and summarized. In order to ascertain the feasibility and applicability of this approach, a comparison is conducted between the results obtained from our proposed method and those obtained from three representative traditional methods. And then, the outcomes obtained from various unwrapping methods in scenarios involving noise and discontinuity, as well as the results between diverse wavelet basis functions, different decomposition layers and distinct iterations, are meticulously analyzed and compared. The findings indicate that our proposed method outperforms traditional phase unwrapping techniques in terms of continuity and smoothness, particularly when exposed to severe noise. Unlike the three classic methods, our proposed method maintains consistent results even in the presence of noise, thereby highlighting its advantages in terms of resilience against noise. In a word, this research serves as a crucial reference for the accurate detection of complex high-temperature flow fields by moiré tomography.

Super-resolution based number-theoretical phase unwrapping method applicable to 2D spiral fringe patterns

Spiral interferometry is a technique that accurately measures changes in 3D structures or refractive indices by converting phase changes into spiral fringe patterns. The spiral fringe patterns consist of phase distributions, which are wrapped from 0 to 2π, requiring phase unwrapping techniques. Phase unwrapping transforms a discontinuous phase image from 0 to 2π into a continuous phase image, which can ultimately be reconstructed into 3D information. The 3D reconstructed information is affected by the unwrapped phase information with noise. Among the phase unwrapping methods, the number-theoretical phase unwrapping method used in 1D structured light is a unique approach that unwraps the phase into a step function. Due to its insensitivity to noise, this method is an effective solution for improving phase unwrapping in noisy environments. However, due to the same characteristics, the resolution inevitably decreases. In this paper, we propose a super-resolution based numerical unwrapping method applicable to two-dimensional spiral patterns. Based on multi-wavelength interpolation, this method not only retains the advantage of the number-theoretical phase unwrapping method, which is insensitive to noise, but also compensates for its disadvantage of resolution degradation. The proposed method uses the basic concept of generating sub-step information by multi-wavelength interpolation and performing super-resolution based on this concept. We perform simulations and experiments to verify the validity. As a result of the verification, it is confirmed that the super-resolution effect of the number-theoretical unwrapping in the 2D spiral fringe patterns can be achieved by the proposed method.

Horizon extraction using absolute seismic phase obtained by unwrapping techniques

Automatic detection of horizons and other geological structures of interest is often employed as a preliminary step in seismic interpretation. Although necessary, the identification and extraction of horizons can be a laborious and time-consuming step for the interpreter. Therefore, we present a semi-automatic horizon extraction algorithm based on the absolute phase of seismic data obtained through phase unwrapping techniques. We assess the algorithm accuracy and robustness in several examples, including noisy data sets. In addition, we present comparative results between two phase unwrapping methods, showing their robustness when associated with seismic horizon extraction. We compare the results obtained by our methods with the results obtained by seismic horizon extraction algorithms available in the literature.

Accurate fringe order recognition with adaptive morphological operations for 3D measurement

Temporal phase unwrapping (TPU) techniques are vulnerable to inaccurate recognition of fringe order due to various factors, including noise, motion blur and defocusing effects. The misalignment between the fringe order and wrapped phase can lead to abnormal jump errors and compromise measuring accuracy. To address this issue, an accurate fringe order recognition method with adaptive morphological operations for 3D measurement is proposed. Differs from the traditional half-period fringe order recognition method, a complete full-flow algorithm is constructed to accurately separate adhesive connected domains, which includes: segmentation and erosion of connected domains, localization of fully eroded connected regions, clustering of separated valid points, and adaptive selection of radius. In contrast to a simplistic morphological open arithmetic, the proposed method has the capability to perform clustering on all separated valid points, thereby achieving lossless fringe order recognition of the full field. And its row-correlation property gives it a larger correctable range than the previous row-independent approach. The experimental results demonstrate the generality, advancement, adaptivity, and precision of our method, built upon the traditional TPUs for obtaining fringe orders.

High-speed 360° 3D shape measurement based on virtual stereo phase unwrapping method

360° three-dimensional (3D) shape measurement is of great significance in the fields of defect detection and reverse modeling. Fringe projection profilometry (FPP) is widely used due to the advantages of high-accuracy and full-field measurement, but the movement of object corrupts the phase measurement. Stereo phase unwrapping (SPU) technique is adopted to improve imaging efficiency, but requires multi-cameras which resulting in high system complexity and cost. In this work, we proposed virtual stereo phase unwrapping (VSPU) method for high-speed 360° 3D shape measurement. This method uses the virtual camera-projector systems formed by the rotation of object for phase unwrapping which only requires single camera-projector to achieve 360° 3D shape measurement. The phase consistency checking in SPU method is modified. Experiments demonstrate that proposed method has strong robustness and can achieve 360° 3D shape measurement in 47 s with an accuracy of 100 μm during continuous rotation of the object.

A Parallel InSAR Phase Unwrapping Method Based on Separated Continuous Regions

Phase unwrapping is an imperative step in interferometry processing that has a significant influence on the quality of subsequent products. Many existing phase unwrapping algorithms have been designed to solve for the unwrapped phase under the assumption that noisy areas with discontinuities are small or that reliable continuity can be recovered there. They attempt to restore the unwrapped phase by using continuity and data quality measures, such as residues. However, when the observing field is divided into separate zones of continuous phase due to a large range of noise, such as those caused by rivers or mountains, it is difficult to use traditional phase unwrapping techniques to recover global continuity in these noisy areas. To address this challenge, we present a two-dimensional parallel phase unwrapping method that is designed to handle cases where the continuity of the phase is separated by closed noisy loops. Based on continuity distances, this method aims to identify continuous regions that are free of hidden phase discontinuities and restore phase continuity between the separated regions. A heterogeneous residual diffusion scheme is used to restore the unwrapped phase outside continuous regions. The parallel algorithm for extracting continuous regions, restoring continuity between the regions, and diffusing residuals was implemented on a GPU device to increase the processing efficiency. We applied our method to typical TanDEM-X data covering rivers, islands, and mountains and demonstrated that it is a promising solution for large-scale, heavily noisy phase unwrapping problems.

Phase Unwrapping using a Joint CNN and SQD-LSTM Network

Phase unwrapping techniques are used in various applications, including Synthetic Aperture Radar (SAR) interferometry (InSAR). Deep learning methods have been recently proposed to tackle this problem. This work aims at explaining and evaluating the method proposed by Perera et al. in [A joint convolutional and spatial quad-directional LSTM network for phase unwrapping, ICASSP 2021]. Furthermore, we provide an online demo to simulate phase images and run them through the network. The network performance can be tested visually and through metrics such as the error standard deviation. The simulation can provide some out-of-distribution data, especially with the added atmospheric signal specific to the InSAR phase. **This is an MLBriefs article, the source code has not been reviewed!**<br> **The original source code is [[available here|https://github.com/Laknath1996/DeepPhaseUnwrap/tree/9316c1b1272c0457000fbbaaff850303d923df88]] (last checked 2022/10/04).**

RFID Gazebo-Based Simulator With RSSI and Phase Signals for UHF Tags Localization and Tracking

Radio Frequency Identification (RFID) technology is becoming very popular in the new era of Industry 4.0, especially for warehouse management, retails, and logistics. RFID systems can be used for objects identification, localization, and tracking, facilitating everyday operators’ efforts. However, the deployment of RFID tags and reader antennas in real-world application scenarios is crucial and takes time. Indeed, deciding where to place tags and/or readers’ requires examining many conditions. If some weaknesses appear in the design, the arrangement must be reconsidered. The proposed work presents a novel open-source RFID simulator that allows modeling environments and testing the deployment of RFID tags and antennas apriori. In such a way, validating the performance of the localization or tracking algorithms in simulation, possible weaknesses that could arise may be fixed before facilities are applied on the field. Any number of tags and antennas can be placed in any position in the created scenario, and the simulator provides the phase and the RSSI signals for each tag. Every reader antenna is parametrized so that different antennas of different vendors can be reproduced. The simulator is implemented as a plugin of Gazebo, a widely used robotic framework integrated with the Robot Operating System (ROS), to reach a broad audience. In order to validate the simulator, a warehouse scenario is modeled, and a tag localization algorithm that uses the phase unwrapping technique and hyperbolae intersection method employing a reader antenna mounted on a mobile robot is used to estimate the position of the tags deployed in the scenario. The outcomes of the experiments showed realistic results.

Array shape calibration with phase unwrapping techniques for highly deformed arrays

Flexible sensor arrays, such as towed and bottom-mounted arrays, typically suffer from large shape deformations, which seriously affect the results of array processing. In this article, an innovative array shape calibration method with phase unwrapping techniques for highly deformed arrays is proposed. The deformed array is divided into several subarrays, and the first subarray is assumed to suffer from slight shape deformations which can be pre-calibrated. With the consideration of highly deformed arrays, uncalibrated sensors in other subarrays would have serious position mismatches. The phase differences between uncalibrated and pre-calibrated sensors are probably larger than 2 π , which lead to phase ambiguity problems. A phase unwrapping technique is proposed to efficiently solve the phase ambiguity problem by considering the physical structure constraints of the deformed array, such as intersensor distance and bending angle. Then, sensor positions in highly deformed arrays are calibrated with multiple target directions. Simulation results evaluate the performance of the proposed calibration method, and the SwellEx-96 shallow water experiment data set is utilised to demonstrate the effectiveness of the proposed method.

Single-shot 3D shape measurement using an end-to-end stereo matching network for speckle projection profilometry.

Speckle projection profilometry (SPP), which establishes the global correspondences between stereo images by projecting only a single speckle pattern, has the advantage of single-shot 3D reconstruction. Nevertheless, SPP suffers from the low matching accuracy of traditional stereo matching algorithms, which fundamentally limits its 3D measurement accuracy. In this work, we propose a single-shot 3D shape measurement method using an end-to-end stereo matching network for SPP. To build a high-quality SPP dataset for training the network, by combining phase-shifting profilometry (PSP) and temporal phase unwrapping techniques, high-precision absolute phase maps can be obtained to generate accurate and dense disparity maps with high completeness as the ground truth by phase matching. For the architecture of the network, a multi-scale residual subnetwork is first leveraged to synchronously extract compact feature tensors with 1/4 resolution from speckle images for constructing the 4D cost volume. Considering that the cost filtering based on 3D convolution is computationally costly, a lightweight 3D U-net network is proposed to implement efficient 4D cost aggregation. In addition, because the disparity maps in the SPP dataset should have valid values only in the foreground, a simple and fast saliency detection network is integrated to avoid predicting the invalid pixels in the occlusions and background regions, thereby implicitly enhancing the matching accuracy for valid pixels. Experiment results demonstrated that the proposed method improves the matching accuracy by about 50% significantly compared with traditional stereo matching methods. Consequently, our method achieves fast and absolute 3D shape measurement with an accuracy of about 100µm through a single speckle pattern.

Novel phase unwrapping technique based on extended information filter

A general framework of a phase unwrapping procedure based on extended information filter is built. Two phase unwrapping algorithms with different observed models, are proposed by combining an extended information filter with an efficient phase gradient estimator, and an efficient quality-guided strategy based on heap-sort. The extended information filter that is a new type of filter with high efficiency and high robustness, is applied to acquire the unambiguous unwrapped phase of wrapped phase images for the first time to our knowledge. Through the application of the extended information filter, simultaneous phase unwrapping and noise suppression have been performed. The efficient phase gradient estimator that has been demonstrated well, is used to efficiently acquire phase gradient information required for the proposed algorithms. The efficient quality-guided strategy based on heap-sort is used to define the path of the proposed algorithms and to guarantee that they efficiently unwrap wrapped pixels along the path, from high-reliance to low-reliance regions. Synthetic and experimental data is used to demonstrate that our proposed algorithms can obtain robust solutions with reasonable time consumption, compared with some of the more traditional algorithms.

Intra Prediction-Based Hologram Phase Component Coding Using Modified Phase Unwrapping

In this paper, we propose a method for compressing the phase component of a full-complex hologram. The JPEG (Joint Photographic Experts Group) Pleno is undergoing standardization for compressing full-complex holograms. If the full-complex hologram is compressed in the form of amplitude and phase components, the three-dimensional information of the hologram may be better preserved. Therefore, in order to solve the disadvantages of the method of independently compressing real and imaginary parts, we propose a method for directly compressing phase information. We select the HEVC (High Efficiency Video Coding), which has the best performance in compressing holograms from previous studies, as the anchor codec, and propose an algorithm for converting the phase information into the form suitable for the HEVC. Since the phase component is very random, we propose a modified phase unwrapping technique to improve this. In addition, in order to make good use of the property of HEVC Intra coding, the phase unwrapping considering Intra prediction is applied, and the most suitable HEVC Intra coding condition is searched. Compared with the result of compressing the phase using the HEVC, the hologram was improved by 2 dB or more and the reconstruction result was improved by more than 4 dB at a compression ratio of 80:1. If the compression ratio is increased, the proposed method has better results.

Smart filtering of phase residues in noisy wrapped holograms

Phase unwrapping is one of the major challenges in multiple branches of science that extract three-dimensional information of objects from wrapped signals. In several applications, it is important to extract the unwrapped information with minimal signal resolution degradation. However, most of the denoising techniques for unwrapping are designed to operate on the entire phase map to remove a limited number of phase residues, and therefore they significantly degrade critical information contained in the image. In this paper, we present a novel, smart, and automatic filtering technique for locally minimizing the number of phase residues in noisy wrapped holograms, based on the phasor average filtering (PAF) of patches around each residue point. Both patch sizes and PAF filters are increased in an iterative algorithm to minimize the number of residues and locally restrict the artifacts caused by filtering to the pixels around the residue pixels. Then, the improved wrapped phase can be unwrapped using a simple phase unwrapping technique. The feasibility of our method is confirmed by filtering, unwrapping, and enhancing the quality of a noisy hologram of neurons; the intensity distribution of the spatial frequencies demonstrates a 40-fold improvement, with respect to previous techniques, in preserving the higher frequencies.

PhaseNet 2.0: Phase Unwrapping of Noisy Data Based on Deep Learning Approach

Phase unwrapping is an ill-posed classical problem in many practical applications of significance such as 3D profiling through fringe projection, synthetic aperture radar and magnetic resonance imaging. Conventional phase unwrapping techniques estimate the phase either by integrating through the confined path (referred to as path-following methods) or by minimizing the energy function between the wrapped phase and the approximated true phase (referred to as minimum-norm approaches). However, these conventional methods have some critical challenges like error accumulation and high computational time and often fail under low SNR conditions. To address these problems, this paper proposes a novel deep learning framework for unwrapping the phase and is referred to as “PhaseNet 2.0”. The phase unwrapping problem is formulated as a dense classification problem and a fully convolutional DenseNet based neural network is trained to predict the wrap-count at each pixel from the wrapped phase maps. To train this network, we simulate arbitrary shapes and propose new loss function that integrates the residues by minimizing the difference of gradients and also uses $L_{1}$ loss to overcome class imbalance problem. The proposed method, unlike our previous approach PhaseNet, does not require post-processing, highly robust to noise, accurately unwraps the phase even at the severe noise level of −5 dB, and can unwrap the phase maps even at relatively high dynamic ranges. Simulation results from the proposed framework are compared with different classes of existing phase unwrapping methods for varying SNR values and discontinuity, and these evaluations demonstrate the advantages of the proposed framework. We also demonstrate the generality of the proposed method on 3D reconstruction of synthetic CAD models that have diverse structures and finer geometric variations. Finally, the proposed method is applied to real-data for 3D profiling of objects using fringe projection technique and digital holographic interferometry. The proposed framework achieves significant improvements over existing methods while being highly efficient with interactive frame-rates on modern GPUs.

Novel broadband measurement technique on PCB cells for the field- and stress-dependent impedance in ferromagnetic wires

The lack of broadband impedance measurements has restricted the potential capabilities of ferromagnetic wire composites, which have been mainly evaluated through theoretical impedance calculated from existing models without considering wire domain microstructure. Here, we have developed an accurate method for measuring the impedance of ferromagnetic wires in a wide frequency range, from 100 kHz up to 15 GHz, under magnetic and stress stimuli. The broadband measurements were ensured by a more accurate microwave calibration on the PCB cell, extending the reference planes up to the wire sample ends and by compensating the sample waveguide properties using the phase unwrapping technique proposed in this work. In addition, a specially designed dogbone PCB measurement cell allows both field- and stress-dependent impedance measurements, efficiently transferring the tensile stress from the cell to the wire sample fixed onto it. The measured wire impedance can be then recalculated into the surface impedance, which constitutes the boundary condition in the antenna equation, describing the microwave scattering properties of a wire. The developed approach will make it possible to build a practically predictive scattering theory in composite materials with embedded wire inclusions and thus their implementation in real-world applications, such as remote stress monitoring.

Pixelated polarizing system for dynamic interferometry events employing a temporal phase unwrapping approach

We describe a robust system to retrieve the phase using a temporal phase unwrapping approach and a pixelated polarizing camera. By considering the characteristics of the polarizing sensor and its capabilities to acquired simultaneously four phase shifted interferograms in a stable manner, we propose the use of a temporal phase unwrapping technique to simplify the phase retrieval procedure in dynamic events. We also show that by combining the polarizing sensor and temporal phase unwrapping algorithms, the phase unwrapping procedure is not only simplified, but also the computing time is reduced one order of magnitude compared with other algorithms. In the approach taken, each pixel is processed independently obtaining the phase difference for a specific time opening the possibility of real-time analysis. Validation experiments are presented.

Performance evaluation and acceleration of Flynn phase unwrapping algorithm using wraps reduction algorithms

Flynn phase unwrapping algorithm, probably, produces the best results in comparison to other methods, but it needs a long execution time. In this paper we suggest combining Flynn algorithm with wraps reduction algorithms in order to reduce its execution time and also improves its noise performance. Additionally, we propose a method that can be used to measure the success of phase unwrapping techniques. Computer simulation and experiments are used to verify the ideas proposed in this paper.

Direction-determined phase unwrapping using geometric constraint of the structured light system: The establishment of minimum phase map

A recently proposed absolute phase unwrapping method using geometric constraints of the structured light system significantly improves the measurement speed and the robustness. The most important step of this method is to create a minimum phase map as the phase unwrapping reference. Current method usually selects the closest plane as the minimum phase map. However, we found that the position of the minimum phase map is direction-determined and it may induce a fatal error to phase unwrapping under certain circumstances. This letter analyzes the direction-determined phase increasing phenomenon and presents a direction-determined phase unwrapping technique, which includes a new establishment method for the minimum phase map and corresponding phase unwrapping procedures.