Phase Unwrapping Research Articles

Review of interferometric synthetic aperture sonar interferometric phase filtering methods

Interferometric synthetic aperture sonar (InSAS) is a novel three dimensional underwater mapping system, which is widely used in various fields. Interferometric phase filtering is a crucial process in InSAS signal processing. The study of interferogram filtering method has great significance to improve the signal-to-noise ratio (SNR) of interferogram, reduce the difficulty of phase unwrapping, and improve the accuracy of digital elevation maps. Firstly, this article introduces the sources of interferometric phase noise. Secondly, it illustrates the difference between real domain filter and complex domain filter by simulation experiment. Thirdly, the various methods of InSAS interferogram filtering are systematically studied, which can be classified into spatial domain filtering and transform domain filtering. The transform domain filtering can be further divided into frequency domain and wavelet transform filtering. Moreover, the advantages and disadvantages of various methods are analyzed theoretically. Finally, numerical simulation and real-data processing experiments are performed, and the advantages and shortcomings of several methods are compared using residue numbers, root mean square error (RMSE), and CPU time as evaluation criteria.

Phase unwrapping based on deep learning in light field fringe projection 3D measurement

Phase unwrapping based on deep learning in light field fringe projection 3D measurement

Full-period fringe order correction method based on dual-threshold cellular automaton

In traditional temporal phase unwrapping (TPU) methods, the fringe order is obtained pixel-to-pixel by multi-frequencies or multi-wavelengths. The direct calculation and error non-accumulation features accelerate the prosperity of TPU. Nevertheless, the noise, defocusing, and non-uniform reflectivity may inevitably lead to some fringe order errors. These errors are powerless against the evolving TPUs such as Gray code and phase coding. In this paper, a full-period fringe order correction method based on dual-threshold cellular automaton is proposed for machine 3D vision. Initially, an advanced dual-threshold cellular automaton algorithm is employed to extract both the strong and weak edges of the wrapped phase individually. Superior to conventional single-threshold edge detection methods, this approach effectively mitigates the edge breakage problem caused by significant height variations. Subsequently, the N-filled map, N-residue mask, and N-start points concepts are introduced to sequentially segment independent connected domains based on the tightly graphical coupling. In addition, by performing edge compensation in the same period, accurate fringe order correction can be achieved even if excessive edge points are identified, as long as the broken edges are effectively connected. The experimental results exhibit exceptional correction performance of the proposed method for intricate isolated objects, objects with non-uniform reflectivity, and dynamic scenes.

Reduced tubuloglomerular feedback activity and absence of its synchronization in a connexin40 knockout rat.

Introduction: Tubuloglomerular feedback (TGF) is the negative feedback component of renal blood flow (RBF) autoregulation. Neighbouring nephrons often exhibit spontaneous TGF oscillation and synchronization mediated by endothelial communication, largely via connexin40 (Cx40). Methods: We had a knockout (KO) rat made that lacks Cx40. One base pair was altered to create a stop codon in exon 1 of Gja5, the gene that encodes Cx40 (the strain is WKY-Gja55em1Mcwi). Blood pressure (BP)-RBF transfer functions probed RBF dynamics and laser speckle imaging interrogated the dynamics of multiple efferent arterioles that reach the surface (star vessels). Results: The distribution of wild type (WT), heterozygote, and KO pups at weaning approximated the Mendelian ratio of 1:2:1; growth did not differ among the three strains. The KO rats were hypertensive. BP-RBF transfer functions showed low gain of the myogenic mechanism and a smaller TGF resonance peak in KO than in WT rats. Laser speckle imaging showed that myogenic mechanism had higher frequency in KO than in WT rats, but similar maximum spectral power. In contrast, the TGF frequency was similar while peak power of its oscillation was much smaller in KO than in WT rats. In WT rats, plots of instantaneous TGF phase revealed BP-independent TGF synchronization among star vessels. The synchronization could be both prolonged and widespread. In KO rats TGF synchronization was not seen, although BP transients could elicit short-lived TGF entrainment. Discussion: Despite the reduced TGF spectral power in KO rats, there was sufficient TGF gain to induce oscillations and therefore enough gain to be effective locally. We conclude that failure to synchronize is dependent, at least in part, on impaired conducted vasomotor responses.

Time-slicing high dynamic range 3D imaging.

Fringe projection profilometry (FPP) has been widely used in 3D measurement due to its high precision and non-contact properties. Nevertheless, it still faces great challenges in measuring scenes with complex reflectivity, in which the dynamic range of the reflected light field of the scene is significantly higher than that of the image detector. In this paper, we propose a time-slicing strategy for high dynamics range 3D imaging by projecting a series of sinusoidal fringe patterns with short and equal length exposure time and performing the fusion of different numbers of short exposure images according to the local gray-value distribution of the images. Moreover, to further improve the measurement efficiency, we realize phase unwrapping using complementary Gray code patterns, which are binary and insensitive to the image sensor's nonlinear response to the reflected light from the scene under test. Experiments are conducted to demonstrate the feasibility and efficiency of the proposed method.

Two-dimensional phase unwrapping based on U2-Net in complex noise environment.

This paper proposes applying the nested U2-Net to a two-dimensional phase unwrapping (PU). PU has been a classic well-posed problem since conventional PU methods are always limited by the Itoh condition. Numerous studies conducted in recent years have discovered that data-driven deep learning techniques can overcome the Itoh constraint and significantly enhance PU performance. However, most deep learning methods have been tested only on Gaussian white noise in a single environment, ignoring the more widespread scattered noise in real phases. The difference in the unwrapping performance of deep network models with different strategies under the interference of different kinds of noise or drastic phase changes is still unknown. This study compares and tests the unwrapping performance of U-Net, DLPU-Net, VUR-Net, PU-GAN, U2-Net, and U2-Netp under the interference of additive Gaussian white noise and multiplicative speckle noise by simulating the complex noise environment in the real samples. It is discovered that the U2-Net composed of U-like residual blocks performs stronger anti-noise performance and structural stability. Meanwhile, the wrapped phase of different heights in a high-level noise environment was trained and tested, and the network model was qualitatively evaluated from three perspectives: the number of model parameters, the amount of floating-point operations, and the speed of PU. Finally, 421 real-phase images were also tested for comparison, including dynamic candle flames, different arrangements of pits, different shapes of grooves, and different shapes of tables. The PU results of all models are quantitatively evaluated by three evaluation metrics (MSE, PSNR, and SSIM). The experimental results demonstrate that U2-Net and the lightweight U2-Netp proposed in this work have higher accuracy, stronger anti-noise performance, and better generalization ability.

3D reconstruction method based on N-step phase unwrapping

3D reconstruction method based on N-step phase unwrapping

Adequate phase unwrapping based on 2[formula omitted] cycle invariant between shifted phase maps

To obtain an adequate unwrapping solution for reliable phase measurement under noisy circumstances, a novel unwrapping algorithm is proposed. This algorithm extracts abundant valid pixels and rejects noise based upon revealing a property of 2π invariant, which is implied between wrapped phase maps with shifted fringe patterns. Distinct from conventional algorithms that use residues or minimum norm solution to attenuate the impacts of noise affected areas, this technique is free from the uncertainties arising from inadequate resources or over-smoothing effects during the unwrapping process. The performance of the proposed algorithm is demonstrated and confirmed through both computer simulations and practical experiments carried out using a fringe projection system. Superior capability in handling noise affected phase images is then achieved.

Improved dynamic distortion correction for fMRI using single-echo EPI and a readout-reversed first image (REFILL).

The boundaries between tissues with different magnetic susceptibilities generate inhomogeneities in the main magnetic field which change over time due to motion, respiration and system instabilities. The dynamically changing field can be measured from the phase of the fMRI data and corrected. However, methods for doing so need multi-echo data, time-consuming reference scans and/or involve error-prone processing steps, such as phase unwrapping, which are difficult to implement robustly on the MRI host. The improved dynamic distortion correction method we propose is based on the phase of the single-echo EPI data acquired for fMRI, phase offsets calculated from a triple-echo, bipolar reference scan of circa 3-10 s duration using a method which avoids the need for phase unwrapping and an additional correction derived from one EPI volume in which the readout direction is reversed. This Reverse-Encoded First Image and Low resoLution reference scan (REFILL) approach is shown to accurately measure B0 as it changes due to shim, motion and respiration, even with large dynamic changes to the field at 7 T, where it led to a > 20% increase in time-series signal to noise ratio compared to data corrected with the classic static approach. fMRI results from REFILL-corrected data were free of stimulus-correlated distortion artefacts seen when data were corrected with static field mapping. The method is insensitive to shim changes and eddy current differences between the reference scan and the fMRI time series, and employs calculation steps that are simple and robust, allowing most data processing to be performed in real time on the scanner image reconstruction computer. These improvements make it feasible to routinely perform dynamic distortion correction in fMRI.

A new approach for nonlinear transient dynamic analysis of micro SMA beam considering size effect and instantaneous phase transformation

Shape Memory Alloys (SMAs) have attracted lots of attraction in the recent years due to their unique characteristics. However, studies in the field of behavior of SMAs at micro scale is not enough and more research is required. The present paper presents a nonlinear dynamic solution for a micro made of NiFeGa SMA, located on a viscoelastic foundation. The recommended approach takes into account instantaneous variations of martensite volume fraction and size effect which are the main novelties of the present study. In this regard, the formulation proposed by Hernandez and Lagoudas is used to capture and model the size effect of the SMAs. The governing differential equations obtained for Euler-Bernoulli micro beam using the Hamilton’s principle, considering the Von-Karman nonlinear strain. The nonlinear equation of motion is solved applying the semi-exact method. In this study, the return mapping convex cutting plane is used, in order to overcome the material nonlinearity of the problem. The obtained results are compared with the reference papers which shows the accuracy of the present model. Results show that with considering the size effect, the loss factor of vibration will increase by increasing the thickness of the micro SMA beam. While regardless of the size effect, this factor remains almost constant. The reason for this phenomenon is that when size effect is taken into account, the thermodynamic properties and critical stresses of phase transformation will change with resizing the SMA. Outputs also show that by increasing the damping coefficient and decreasing the stiffness of foundation, more energy is wasted in the vibration of the micro SMA beam. In addition, it was observed that micro beams with lower thicknesses are more sensitive to foundation characteristics meanwhile the loss factor of vibration with lesser thicknesses changes more by changing the foundation stiffness and damping coefficients.

Moving sound source localization and tracking for an autonomous robot equipped with a self-rotating bi-microphone array.

In this paper, we present two approaches to localizing and tracking a sound source that moves in a three-dimensional (3D) space. The sound signal was captured by a unique bi-microphone system that rotates at a constant angular velocity. The motion of the sound source along with the rotation of the bi-microphone array produces a sinusoidal inter-channel distance difference (ICDD) signal with time-varying amplitude and phase. Four state-space models were developed and employed to design extended Kalman filters (EKFs) that identify instantaneous amplitude and phase of the ICDD signal. Both theoretical and numerical observability analyses of the four state-space models were performed to reveal singularities of the proposed EKFs in the domain of interest. We also developed a Hilbert-transform based method that localizes the sound source by comparing the true analytic ICDD signal to a virtual reference signal with zero elevation and azimuth angles. A moving average filter is then applied to reduce the noise and the effect of the artifacts at the beginning and the ending portions of the estimates. The effectiveness of the proposed methods was evaluated using comparison studies in simulation.

Phase Unwrapping of Color Doppler Echocardiography using Deep Learning.

Color Doppler echocardiography is a widely used non-invasive imaging modality that provides real-time information about the intracardiac blood flow. In an apical long-axis view of the left ventricle, color Doppler is subject to phase wrapping, or aliasing, especially during cardiac filling and ejection. When setting up quantitative methods based on color Doppler, it is necessary to correct this wrapping artifact. We developed an unfolded primal-dual network to unwrap (dealias) color Doppler echocardiographic images and compared its effectiveness against two state-of-the-art segmentation approaches based on nnU-Net and transformer models. We trained and evaluated the performance of each method on an in-house dataset and found that the nnU-Net-based method provided the best dealiased results, followed by the primal-dual approach and the transformer-based technique. Noteworthy, the primal-dual network, which had significantly fewer trainable parameters, performed competitively with respect to the other two methods, demonstrating the high potential of deep unfolding methods. Our results suggest that deep learning-based methods can effectively remove aliasing artifacts in color Doppler echocardiographic images, outperforming DeAN, a state-of-the-art semi-automatic technique. Overall, our results show that deep learning-based methods have the potential to effectively preprocess color Doppler images for downstream quantitative analysis.

Bridge damage analysis under joint environmental and operational variability

One of the main challenges for bridge damage identification using monitoring data is to acquire sensitive damage features but insensitive to operational and environmental effects as well as noise. Specifically, the temperature as part of environmental variability can mask structural damages in bridges. Principal Component Analysis (PCA) has been applied here as a well-known and robust technique for removing environmental variability and obtain damage-sensitive indices. As a first aim, PCA is used considering only ambient vibrations and the natural frequencies are considered as damage indicators. As a second objective, PCA in conjunction with Hilbert Huang Transform (HHT) and Variational Mode Decomposition (VMD) are applied to eliminate the environmental influence in transient vibrations due to traffic. The combined methodology is applied to the case of a numerical benchmark by using the Instantaneous Phase Difference (IPD) as novel vibration damage feature in the case of non-stationary vibrations. The results show that the proposed strategy to use the non-stationary vibration due to traffic instead of ambient vibration seems a promising tool for damage identification and, therefore, its capabilities in real bridge applications are worth exploring further when experimental data from real bridges will become available.

Magnetic properties of iron-filled hydrogel clusters: a model system for quantitative susceptibility mapping with MRI

Quantitative approaches in clinical Magnetic Resonance Imaging (MRI) benefit from the availability of adequate phantoms. Ideally, the phantom material should reflect the complexity of signals encountered in vivo. In the present study we validate and characterize clusters consisting of sodium-polyacrylate embedded in an alginate matrix that are unloaded or loaded with iron for Quantitative Susceptibility Mapping (QSM), yielding a non-uniform iron distribution and tissue-mimicking MRI properties. Vibrating sample magnetometry (VSM) was used to characterize the phantom material and verify the accuracy of previous MRI-based observations of the QSM-based molar susceptibility (χM). MRI at 14.1 T with high resolution acquisitions was used to determine the size of hydrogel clusters and to further investigate the suitability of the phantom material as a model system for QSM at high field. VSM demonstrated that the iron-solution used for manufacturing the phantoms consisted of ferric iron. The χM of clusters with a constant iron-to-polyacrylate-ratio (8.3 μg/mg) observed with VSM was 50.7 ± 8.0 ppb mM−1 but showed a tendency towards saturation at total iron concentrations >1 mM. On unwrapped and background corrected phase-images obtained with gradient-echo MRI and an isotropic voxel size of 37 μm at 14.1T, the iron-free clusters had a roundish shape and blurry border with an equivalent sphere diameter of 276 ± 230 µm and a QSM of 7 ± 7 ppb. Iron-loading led to strong phase wrapping, necessitating the use of short echo times, or short inter-echo delays below 10 ms at 14.1 T. The equivalent sphere diameter of the iron-loaded clusters was estimated to 400–500 µm as verified using different MRI modalities (spin-echo, inversion recovery, and gradient echo MRI). With a constant iron-to-polyacrylate ratio, the cluster density was 10 mm−3 mM−1 iron. In agreement with previous observations, χM of samples with a constant amount of polyacrylate was 50.6 ± 11.4 ppb mM−1 at 3 T while samples containing clusters with a constant iron-to-polyacrylate-ratio yielded χM = 56.1 ± 6.3 ppb mM−1 at 3T and 55.6 ± 0.7 ppb mM−1 at 14.1 T. In conclusion we found that the molar susceptibility of the proposed model system corresponds to that predicted for ferritin in vivo loaded with 3000 iron atoms. The reproducibility was within 12% across MR scanners, batches, and phantom types and compared well with results obtained with vibrating sample magnetometry.

Wavelet extraction using cepstrum

Cepstrum-based deconvolution can be a powerful tool to enhance the resolution of seismic data by removing multiples or sharpening the wavelets in the seismic data. In the past, it has been tested under the assumption that subsurface reflectivity sequences are minimum phase. However, the minimum phase requirement may be too restrictive to be used for seismic data acquired for oil and gas exploration. When the reflectivity sequence is not minimum phase, phase wrapping severely impacts the phase of the wavelet with the phase of the reflectivity sequence. We have examined the effect of phase wrapping by using two wavelets and a reflectivity sequence that was not minimum phase. Upon comparing the two cepstra, the cepstrum directly from the trace and the desired cepstrum, we find that the difference between the two cepstra indicated an odd symmetry near the zero quefrency and devise a way to make the cepstrum from the trace close to the desired cepstrum if the wavelet does not undergo its own phase wrapping. This scheme allows for extracting the correct wavelet, which was used for deconvolution to recover the reflectivity sequence. We apply the scheme to a shot gather from a shallow marine environment to extract the wavelets and deconvolve the data with the extracted wavelets. The deconvolved shot gather indicates much enhanced resolution and the wavelets appear closer to zero phase than the wavelets in the gather before deconvolution. Because air-gun arrays usually generate a source wavelet that does not have its own phase wrapping, cepstrum-based approaches can be a viable tool to extract a wavelet from marine seismic data for subsequent processing.

A new method and application of groundwater prediction along the direction of tunnel excavation in karst strata

Abstract Tunnel construction in karst strata with abundant water causes changes in the surrounding groundwater environment, which can easily trigger geological disasters such as mud and water inrush. How to accurately predict the groundwater ahead of tunnel excavation face is a highly challenging problem. In order to improve the detection accuracy of groundwater during the construction of a deep buried tunnel, the transmission and reflection process of seismic waves at the interface and the relationship between the reflection coefficient and seismic wave signal have been analyzed on the basis of a two-phase medium theory in this paper. The expression of seismic wave stress–response relationship associated with the instantaneous amplitude and instantaneous phase and frequency is established. Then the relationship between seismic wave attributes and groundwater seepage potential energy is derived by combining the fluid mechanics theory, which is used as the basis for the determination and identification of groundwater volume and classified, and a new technology of an advanced detection of groundwater by seismic waves is established. This method has been applied to the Zhanghuai Railway in China and quantitatively predicted the karst water and caves in the Tianqiaoshan Tunnel before excavation. The engineering test proves the reliability and advancement of this technology.

Phase and amplitude, two sides of functional connectivity.

The dynamics of the human brain can be captured by estimating time-resolved functional network connectivity (trFNC). The most used method for estimating trFNC is sliding window Pearson correlation (SWPC). Methods based on instantaneous phase synchrony, which uses phase information for estimating trFNC are being increasingly used. These two approaches are similar under specific assumptions. Prior works have focused on which of these approaches is the best. Some works argue that SWPC can capture amplitude information and therefore we believe that instantaneous phase synchrony methods and SWPC capture different aspects of connectivity since phase synchrony methods work with the phase of the signal. Here we show that these two approaches result in different time-resolved information and therefore should be viewed as complimentary views of connectivity.

Functional Connectivity Analysis in Multi-channel EEG for Emotion Detection with Phase Locking Value and 3D CNN.

The noise-assisted multivariate Empirical mode decomposition (NA-MEMD) is applied to multi-channel EEG signals to obtain narrow-band scale-aligned intrinsic mode functions (IMFs) upon which functional connectivity analysis is performed. The connectivity pattern in relation to inherent functional activity of brain is estimated with the phase locking value (PLV). Instantaneous phase difference among different EEG channels gives PLV that is used to build the functional connectivity map. The connectivity map yields spatial-temporal feature representation which is taken as input of the proposed emotion detection system. The spatial-temporal features can be learned with a 3D convolutional neural network for classifying emotion states. The proposed system is evaluated on two publicly available DEAP and SEED dataset for binary and multi-class emotion classification. On detecting low versus high level in the valence and arousal dimensions, the attained accuracy values are 97.37% and 96.26% respectively. Meanwhile, this system yields 94.78% and 99.54% accuracy on multi-class task on DEAP and SEED, which outperform previously reported systems with other deep learning models and conventional EEG features.

Point-cloud acquisition in CFRP composites using ultrasonic location estimation with the phase-shift reference pulse

Wrinkles in carbon fiber reinforced plastics (CFRP) degrade the mechanical performance. The numerical study on wrinkles requires internal structural point cloud for the meso-structure reconstruction. This paper explores the ultrasonic location estimation with the phase-shift reference pulse for the point-cloud acquisition. The point-cloud acquisition using pulse-echo signals is a time-delay estimation which is a multi-reflection and multi-delay problem. We theoretically simplify the multi-reflection problem as a single-reflection problem and propose a normalized-cross-correlation-peaks (NCCPeaks) method for the multi-delay problem. The proposed method can eliminate some amplitude decrease and balance the smearing and frequency-dependent effects. Simulation shows that the proposed method has the maximum detectable depth without missing inter-ply estimations and a stronger noise resistance than the instantaneous phase method. An experiment is implemented on the 32-ply CFRP sample with an induced wrinkle. The estimation results of the instantaneous phase and NCCPeaks methods are almost the same at the first thirteenth layers. After the thirteenth layer, the NCCPeaks method has a stabler estimation and lower false estimation index than the instantaneous phase method.

A Markov random field based method for removing invalid unwrapping phase points in 3D reconstruction

AbstractFringe projection profilometry is widely used in 3D structured light due to its fast speed and accuracy. However, in the process of phase unwrapping, it is easy to cause invalid points in the edges and shadows of objects, which leads to error points in 3D reconstruction. To solve this problem, we propose an invalid points removal method based on Markov random fields. Specifically, the proposed method formulates unwrapped phase and mask maps as energy functions and uses iterative methods to minimize them. Furthermore, we validate the proposed method in a monocular structured light system and compare it with existing algorithms. Results show that the proposed method effectively identifies edges and shadows while preserving valid points, and has strong robustness and correctness.