Accurate Phase Unwrapping Research Articles

An Anti-Noise-Designed Residual Phase Unwrapping Neural Network for Digital Speckle Pattern Interferometry

DSPI (Digital Speckle Pattern Interferometry) is a non-destructive optical measurement technique that obtains phase information of an object through phase unwrapping. Traditional phase unwrapping algorithms depend on the quality of the images, which demands preprocessing such as filtering and denoising. Moreover, the unwrapping time is highly influenced by the size of the images. In this study, we proposed a new deep learning-based phase unwrapping algorithm combining the residual network and U-Net network. Additionally, we incorporated an improved SSIM function as the loss function based on camera characteristics. The experimental results demonstrated that the proposed method achieved higher quality in highly noisy phase unwrapping maps compared to traditional algorithms, with SSIM values consistently above 0.98. In addition, we applied image stitching to the network to process maps of various sizes and the unwrapping time remained around 1 s even for larger images. In conclusion, our proposed network is able to achieve efficient and accurate phase unwrapping.

A new 3D phase unwrapping method by region partitioning and local polynomial modeling in abdominal quantitative susceptibility mapping.

Accurate phase unwrapping is a critical prerequisite for successful applications in phase-related MRI, including quantitative susceptibility mapping (QSM) and susceptibility weighted imaging. However, many existing 3D phase unwrapping algorithms face challenges in the presence of severe noise, rapidly changing phase, and open-end cutline. In this study, we introduce a novel 3D phase unwrapping approach utilizing region partitioning and a local polynomial model. Initially, the method leverages phase partitioning to create initial regions. Noisy voxels connecting areas within these regions are excluded and grouped into residual voxels. The connected regions within the region of interest are then reidentified and categorized into blocks and residual voxels based on voxel count thresholds. Subsequently, the method sequentially performs inter-block and residual voxel phase unwrapping using the local polynomial model. The proposed method was evaluated on simulation and in vivo abdominal QSM data, and was compared with the classical Region-growing, Laplacian_based, Graph-cut, and PRELUDE methods. Simulation experiments, conducted under different signal-to-noise ratios and phase change levels, consistently demonstrate that the proposed method achieves accurate unwrapping results, with mean error ratios not exceeding 0.01%. In contrast, the error ratios of Region-growing (N/A, 84.47%), Laplacian_based (20.65%, N/A), Graph-cut (2.26%, 20.71%), and PRELUDE (4.28%, 10.33%) methods are all substantially higher than those of the proposed method. In vivo abdominal QSM experiments further confirm the effectiveness of the proposed method in unwrapping phase data and successfully reconstructing susceptibility maps, even in scenarios with significant noise, rapidly changing phase, and open-end cutline in a large field of view. The proposed method demonstrates robust and accurate phase unwrapping capabilities, positioning it as a promising option for abdominal QSM applications.

MR Elastography With Optimization-Based Phase Unwrapping and Traveling Wave Expansion-Based Neural Network (TWENN).

Magnetic Resonance Elastography (MRE) can characterize biomechanical properties of soft tissue for disease diagnosis and treatment planning. However, complicated wavefields acquired from MRE coupled with noise pose challenges for accurate displacement extraction and modulus estimation. Using optimization-based displacement extraction and Traveling Wave Expansion-based Neural Network (TWENN) modulus estimation, we propose a new pipeline for processing MRE images. An objective function with Dual Data Consistency (Dual-DC) has been used to ensure accurate phase unwrapping and displacement extraction. For the estimation of complex wavenumbers, a complex-valued neural network with displacement covariance as an input has been developed. A model of traveling wave expansion is used to generate training datasets for the network with varying levels of noise. The complex shear modulus map is obtained through fusion of multifrequency and multidirectional data. Validation using brain and liver simulation images demonstrates the practical value of the proposed pipeline, which can estimate the biomechanical properties with minimal root-mean-square errors when compared to state-of-the-art methods. Applications of the proposed method for processing MRE images of phantom, brain, and liver reveal clear anatomical features, robustness to noise, and good generalizability of the pipeline.

Single-frequency and accurate phase unwrapping method using deep learning

Phase unwrapping is an important part of fringe projection profilometry(FPP), which greatly affects the efficiency and accuracy of reconstruction. Phase unwrapping methods with deep learning achieve single-frequency phase unwrapping without additional cameras. However, existing methods have low accuracy in the real complex scene, and can not process data whose resolution is greater than the resolution of training data. This paper introduces a neural convolutional network named as VRNet which achieves accurate and single-frequency phase unwrapping without extra cameras. VRNet with encoder-decoder structure gets multi-scale feature maps through feeding the wrapped phase map into the encoder, then fuses the feature maps recursively by using the proposed feature fusion module to accomplish precise prediction. In order to further improve the accuracy of phase unwrapping, this paper presents a phase correction method based on the distribution characteristics of the absolute phase. The method divides the cross-section of the absolute phase map into several curves and identifies a misclassified pixel by comparing its absolute phase value with the value of neighboring curves. In contrast to existing methods, the method is row-independent and does not require segmentation of image. Moreover, this paper accomplishes the prediction of high-resolution data through the phase stitching strategy and fine-tuning the phase correction method. Extensive experiments show that the proposed method is able to achieve high-accuracy and single-frequency phase unwrapping in real scenes which consist of at least one complex object, and is also effective for wrapped phase maps with a resolution larger than the training data.

A Multi-Task Learning for 2D Phase Unwrapping in Fringe Projection

Phase unwrapping is a challenging task in signal processing, spanning its applications in optical metrology, SAR interferometry, and many other signal reconstruction tasks. Fringe Projection Profilometry is a popular active-sensing approach for generating high-resolution three-dimensional (3D) surface information in which phase unwrapping is a crucial step. This letter proposes a multi-task learning-based phase unwrapping method for simultaneous denoising and wrap-count prediction in fringe projection. The proposed network, referred to as TriNet, has nested pyramidal architecture with a single encoder and two decoders, all connected through skip connections. The proposed approach does not require any pre-processing for noise removal like the conventional methods or any post-processing such as smoothing, like in existing deep learning methods but results in a quite accurate phase unwrapping. The proposed method outperforms the existing and state-of-the-art methods for the 3D reconstruction task in Fringe Projection by a significant margin even in the presence of very high noise.

An Improved Phase Unwrapping Method Based on Hierarchical Networking and Constrained Adjustment

Accurate phase unwrapping (PU) is a precondition and key for using synthetic aperture radar interferometry (InSAR) technology to successfully invert topography and monitor surface deformations. However, most interferograms are seriously polluted by noise in the low-quality regions, which poses difficulties for PU. Therefore, using the strategy of leveling network adjustment, this paper proposes an improved PU method based on hierarchical networking and constrained adjustment. This method not only limits the phase error transfer of low-quality points, but also takes the PU results of high-quality points as control points and uses the network adjustment method with constraints to unwrap low-quality points, which effectively inhibits the influence of noise and improves the accuracy of unwrapping. Regardless of the unwrapping method used for high-quality points, the unwrapping accuracy of low-quality points can always be improved. Compared with other traditional two-dimensional phase unwrapping workflows, this method can more accurately recover the phase of low-coherence regions only through the interferogram. A simulation experiment showed that the local noise of the interferogram was effectively inhibited, and the PU accuracy of the low-quality regions was improved by 16–46% compared with different traditional methods. For a real-data experiment of mining area with low coherence, the PU result of our proposed method had fewer residues and lower phase standard deviation than traditional methods, further indicating the practicability and robustness of the proposed method. The work in this paper has considerable practical significance for recovering the decoherence phase with serious local noise such as mining centers and groundwater subsidence centers.

Phase unwrapping of digital holographic microscopy using adaptive region segmentation and phase derivative calibration with respect to fringe density

Accurate phase unwrapping of the wrapped phase maps with high noise and uneven fringe densities is an essential problem for phase restoration in digital holographic microscopy. In this paper, a phase unwrapping algorithm using adaptive region segmentation and phase derivative calibration with respect to fringe density is proposed. The dense and sparse fringe regions of the wrapped phase map are adaptively segmented by using the sine/cosine spatial filtering and calculating the second-order phase gradient. Then, the first-order spatial wrapped phase derivative maps are divided into four phase derivative maps, and the phase anomalies on them are calibrated respectively. Finally, the four maps were recombined into two new phase derivative maps, and the unweighted least-squares iterative algorithm is implemented to obtain the continuous phase map. The advantage of our algorithm is that it can detect, calibrate and restore the phase anomalies based on fringe density automatically. Simulation and experimental results demonstrated that the proposed algorithm has better accuracy and effectiveness in dealing with the wrapped phase maps with high fringe density and high noise, which indicates that our algorithm is able to process the wrapped phase maps corrupted by coherent noise and phase aberration in the digital holographic microscopy.

Adaptive mask generating algorithm based on the fuzzy set theory for the weighted least-squares phase unwrapping

In the digital speckle pattern interferometry (DSPI), accurate phase unwrapping is essential for quantitative phase measurement. In this paper, a novel adaptive mask generating algorithm based on the fuzzy set theory is proposed, which can automatically calculate an optimal threshold for the reliability masked weighted least-squares phase unwrapping. The reliability map of a wrapped phase map is firstly calculated based on the second differences of each pixel. Then, the fuzzy interval of the threshold is determined according to reliability values of the residues and standard deviation of the reliability map, and a membership function describing the fuzzy threshold is established to map the reliability values to the interval of [0, 1]. At last, the membership matrix is used to perform weighted average processing on the reliability map to automatically calculate the optimal threshold for generating a 0-1 mask. Two sets of simulated phase maps under different noise levels and fringe abnormal conditions are generated to evaluate and the accuracy of the adaptive threshold and the performance of the proposed algorithm. Experimental phase data of deformation dynamic measurement in DSPI is adopted to verify the effectiveness of the proposed algorithm. Simulation and experimental results show that the algorithm can adaptively calculate an optimal threshold of different wrapped phase maps, which is very close to the threshold elaborately selected by manual intervention, and can provide a reliable and accurate unwrapping phase for actual phase measurement.

Direct and accurate phase unwrapping with deep neural network.

In this paper a novel, to the best of our knowledge, deep neural network (DNN), VUR-Net, is proposed to realize direct and accurate phase unwrapping. The VUR-Net employs a relatively large number of filters in each layer and adopts alternately two types of residual blocks throughout the network, distinguishing it from the previously reported ones. The proposed method enables the wrapped phase map to be unwrapped precisely without any preprocessing or postprocessing operations, even though the map has been degraded by various adverse factors, such as noise, undersampling, deforming, and so on. We compared the VUR-Net with another two state-of-the-art phase unwrapping DNNs, and the corresponding results manifest that our proposal markedly outperforms its counterparts in both accuracy and robustness. In addition, we also developed two new indices to evaluate the phase unwrapping. These indices are proved to be effective and powerful as good candidates for estimating the quality of phase unwrapping.

SPUD: simultaneous phase unwrapping and denoising algorithm for phase imaging.

Recent methods for phase unwrapping in the presence of noise include denoising algorithms to filter out noise as a preprocessing stage. However, including a denoising stage increases the overall computational complexity resulting in long execution times. In this paper, we present a noniterative simultaneous phase unwrapping and denoising algorithm for phase imaging, referred to as SPUD. The proposed method relies on the least squares discrete cosine transform (DCT) solution for phase unwrapping with an additional sparsity constraint on the DCT coefficients of the unwrapped solution. Simulation results with different levels of noise and wrapped phase fringe density reveal the suitability of the proposed method for accurate phase unwrapping and restoration. When compared to the 2D windowed Fourier transform filter, SPUD performs better in terms of phase error and execution times. The processing of experimental data from synthetic aperture radar showed the capability for processing real images, including removing phase dislocations. An implementation of the proposed algorithm can be accessed and executed through a Code Ocean compute capsule.

An arc-clustering-based phase ambiguity estimation method for persistent scatterer interferometry

ABSTRACTThe reliability of persistent scatterer interferometry (PSI) is directly related to the accurate phase unwrapping (PU) of the 3-D (2-D space and time) sparse data stack. Phase ambiguities estimated using temporal phase unwrapping (TPU) are crucially exploited in most 3-D PU algorithms. However, most TPU methods are not noise-robust owing to the independent processing of each arc in the persistent scatterer network. To solve this problem, the cluster-analysis-based PU method for digital elevation model (DEM) construction is adapted to the phase ambiguity estimation problem for PSI in this letter. First, for each arc, the interior relation among phase ambiguities in multiple interferograms is derived to be linear and can be represented by an intercept vector. Subsequently, arcs with the same ambiguities are clustered according to their intercept vectors because arcs with identical phase ambiguities are verified to have the same intercept vectors. Moreover, a more reliable intercept vector can be calculated for each arc cluster by combining the intercept vectors within the cluster. Finally, more precise phase differences are estimated for each cluster using the corresponding intercept vector so that all the arcs are better unwrapped. Both the simulated and real experiments indicate the effectiveness and superiority of the proposed algorithm.

Phase unwrapping in dual-wavelength digital holographic microscopy with total variation regularization.

A two-step dual-wavelength phase imaging method with total variation (TV) regularization in digital holographic microscopy (DHM) is presented. The rough height map is first denoised with TV regularization, and then it is used as a guiding map for accurate phase unwrapping. By combining the principle of dual-wavelength interferometry and TV regularization, the problem of phase unwrapping is converted into a minimization problem that can be efficiently solved with the Split Bregman algorithm. The proposed algorithm allows a synthetic wavelength that can be arbitrarily large in principle to a single wavelength, while the accuracy of the phase map can achieve the same level in single-wavelength DHM. Moreover, the unwrapping method is robust to the change of weighting parameters. Comparative topographic measurements of a sample with abrupt steps are illustrated, and the results verified the effectiveness of the method.

Hybrid Random Walk-Linear Discriminant Analysis Method for Unwrapping Quantitative Phase Images of Biological Samples

Quantitative phase imaging (QPI) of biological specimens is an emerging approach that uses the phase shift of light as it passes through living cells to extract biophysical properties, such as cell dry mass and the intracellular distribution of mass. Previous QPI applications include measurement of red blood cell mechanical properties and drug resistance of a heterogeneous cancer cell population. An essential part of processing any QPI dataset is phase unwrapping, the removal of phase ambiguities inherent to QPI. Classical phase unwrapping algorithms, such as the widely-used Goldstein algorithm, are often inadequate for biological samples, due to cells’ varying morphology and because cell optical pathlength often exceeds one wavelength of visible light. We present a new phase unwrapping algorithm, the hybrid random walk-linear discriminant analysis (HRL) method, for correcting phase ambiguities where standard algorithms have failed. HRL makes two key assumptions about QPI biological data based on previous observations: cell optical path length is never less than zero; and uncorrected regions are predominantly one wavelength lower than the correct level. These constraints are applied to Goldstein-unwrapped QPI data using a biased random walk based on a linear discriminant analysis (LDA)-generated image, which emphasizes the edges of cells and phase-wrapped regions. A genetic algorithm is then applied to fine-tune the LDA coefficients. The HRL method results in highly accurate (area under curve = 0.999) phase unwrapping of biological QPI data. Our ongoing work measures mass changes in cytotoxic T cells and target cancer cells using accurate phase unwrapping to identify T cells capable of tumor-specific killing for use in cancer immunotherapy. The general procedure of image segmentation based on HRL enables precise identification of cell edges and may have applications for many other imaging approaches beyond QPI techniques.

Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique.

A phase unwrapping algorithm for interferometric fringes based on the unscented Kalman filter (UKF) technique is proposed. The algorithm can bring about accurate phase unwrapping and good noise suppression simultaneously by incorporating the true phase and its derivative in the state vector estimation through the UKF process. Simulations indicate that the proposed algorithm has better accuracy than some widely employed phase unwrapping approaches in the same noise condition. Also, the time consumption of the algorithm is reasonably acceptable. Applications of the algorithm in our different optical interferometer systems are provided to demonstrate its practicability with good performance. We hope this algorithm can be a practical approach that can help to reduce the systematic errors significantly induced by phase unwrapping process for interferometric measurements such as wavefront distortion testing, surface figure testing of optics, etc.

Exact computation of the unwrapped phase of finite-length time series

R. McGowan and R. Kuc recently (IEEE Trans. Acoust., Speech, Signal Processing, vol.ASSP-30, p.719 (1982)) showed that a direct relationship between a time series and its unwrapped phase exists. They proposed an algorithm for computing the unwrapped phase by counting the number of sign changes in a Sturm sequence generated from the real and imaginary parts of the discrete Fourier transform. Their algorithm is limited to relatively short sequences by numerical accuracy. An extension of their algorithm is proposed which, by using all-integer arithmetic, permits exact computation of the number of multiples of pi required to determine the unwrapped phase for rational-valued time sequences of arbitrary length. Since the computation is exact, the extended numerical algorithm should be of interest when accurate phase unwrapping is required.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>