Tile-Based Two-Dimensional Phase Unwrapping for Digital Holography Using a Modular Framework

A variety of physical and biomedical imaging techniques, such as digital holography, interferometric synthetic aperture radar (InSAR), or magnetic resonance imaging (MRI) enable measurement of the phase of a physical quantity additionally to its amplitude. However, the phase can commonly only be measured modulo 2π, as a so called wrapped phase map. Phase unwrapping is the process of obtaining the underlying physical phase map from the wrapped phase. Tile-based phase unwrapping algorithms operate by first tessellating the phase map, then unwrapping individual tiles, and finally merging them to a continuous phase map. They can be implemented computationally efficiently and are robust to noise. However, they are prone to failure in the presence of phase residues or erroneous unwraps of single tiles. We tried to overcome these shortcomings by creating novel tile unwrapping and merging algorithms as well as creating a framework that allows to combine them in modular fashion. To increase the robustness of the tile unwrapping step, we implemented a model-based algorithm that makes efficient use of linear algebra to unwrap individual tiles. Furthermore, we adapted an established pixel-based unwrapping algorithm to create a quality guided tile merger. These original algorithms as well as previously existing ones were implemented in a modular phase unwrapping C++ framework. By examining different combinations of unwrapping and merging algorithms we compared our method to existing approaches. We could show that the appropriate choice of unwrapping and merging algorithms can significantly improve the unwrapped result in the presence of phase residues and noise. Beyond that, our modular framework allows for efficient design and test of new tile-based phase unwrapping algorithms. The software developed in this study is freely available

Phase unwrapping using a regular mesh grid

Phase unwrapping is a key step in the fringe pattern analysis. Although there are many algorithms for recovering continuous phase from wrapped phase maps, many of them are computationaly heavy, even for smooth phase maps. The smoothness characteristics of a phase map allow the use of radial basis functions to model the unwrapped phase. This method helps to reduce the processing time when unwrapping the phase. The processing time can be reduced even more when the reconstruction does not take into account all the pixels of the phase map image. In this paper we describe an algorithm for phase unwrapping where the phase map is reconstructed from a subset of pixels of the phase image using radial basis functions (RBFs). The proposed method is compared with the algorithm based on the same radial basis functions (RBFs) but using all the phase image pixels

K-space data processing for Magnetic Resonance Elastography (MRE)

International audienceObject: Magnetic Resonance Elastography (MRE) requires substantial data processing based on phase image reconstruction, wave enhancement and inverse problem solving. The objective of this study is to propose a new, fast MRE method based on MR raw data processing, particularly adapted to applications requiring fast MRE measurement or high elastogram update rate.Material and Methods: The proposed method allows measuring tissue elasticity directly from raw data without prior phase image reconstruction and without phase unwrapping. Experimental feasibility is assessed both in a gelatin phantom and in the liver of a porcine model in vivo. Elastograms are reconstructed with the raw MRE method and compared to those obtained using conventional MRE. In a third experiment, changes in elasticity are monitored in real-time in a gelatin phantom during its solidification by using both conventional MRE and raw MRE.Results: The raw MRE method shows promising results by providing similar elasticity values to the ones obtained with conventional MRE methods while decreasing the number of processing steps and circumventing the delicate step of phase unwrapping. Limitations of the proposed method are the influence of the magnitude on the elastogram and the requirement for a minimum number of phase offsets.Conclusion: This study demonstrates the feasibility of directly reconstructing elastograms from raw data

A Novel Phase Unwrapping Method for Low Coherence Interferograms in Coal Mining Areas Based on a Fully Convolutional Neural Network

\ua9 2008-2012 IEEE. Subsidence caused by underground coal mining activities seriously threatens the safety of surface buildings, and interferometric synthetic aperture radar has proven to be one effective tool for subsidence monitoring in mining areas. However, the environmental characteristics of mining areas and the deformation behavior of mining subsidence lead to low coherence of interferogram. In this case, traditional phase unwrapping methods have problems, such as low accuracy, and often fail to obtain correct deformation information. Therefore, a novel phase unwrapping method is proposed using a channel-attention-based fully convolutional neural network (FCNet-CA) for low coherence mining areas, which integrates multiscale feature extraction block, bottleneck block, and can better extract interferometric phase features from the noise. In addition, based on the mining subsidence prediction model and transfer learning method, a new sample generation strategy is proposed, making the training dataset feature information more diverse and closer to the actual scene. Simulation experiment results demonstrate that FCNet-CA can restore the deformation pattern and magnitude in scenarios with high noise and fringe density (even if the phase gradient exceeds π). FCNet-CA was also applied to the Shilawusu coal mining area in Inner Mongolia Autonomous Region, China. The experimental results show that, compared with the root mean square error (RMSE) of phase unwrapping network and minimum cost flow, the RMSE of FCNet-CA in the strike direction is reduced by 67.9% and 29.5%, respectively, and by 72.4% and 50.9% in the dip direction, respectively. The actual experimental results further verify the feasibility and effectiveness of FCNet-CA

Assessment of learning tomography using Mie theory

In Optical diffraction tomography, the multiply scattered field is a nonlinear function of the refractive index of the object. The Rytov method is a linear approximation of the forward model, and is commonly used to reconstruct images. Recently, we introduced a reconstruction method based on the Beam Propagation Method (BPM) that takes the nonlinearity into account. We refer to this method as Learning Tomography (LT). In this paper, we carry out simulations in order to assess the performance of LT over the linear iterative method. Each algorithm has been rigorously assessed for spherical objects, with synthetic data generated using the Mie theory. By varying the RI contrast and the size of the objects, we show that the LT reconstruction is more accurate and robust than the reconstruction based on the linear model. In addition, we show that LT is able to correct distortion that is evident in Rytov approximation due to limitations in phase unwrapping. More importantly, the capacity of LT in handling multiple scattering problem are demonstrated by simulations of multiple cylinders using the Mie theory and confirmed by experimental results of two spheres

Weighted multi-resolution phase-unwrapping method

The proposed method for phase unwrapping is based on a global analysis of the interferometrical phase. The underlying principle is that the interferogram is partitioned such that the unwrapped-phase function on each element can be locally modelled by the mean values of the phase difference between neighbouring pixels in azimuth and range directions. Using this local information and a least-squares algorithm (Gauss-Seidel relaxation), an approximate model of the unwrapped phase is then generated and tested by calculating the “residue image” defined as the difference between the original interferogram and the model itself. If there are residual fringes, then the result must be iteratively refined applying the method to the residue image. The accuracy of the proposed estimation depends on the dimensions of the elements and the dynamic content of the phase, i.e. on the “roughness” of the ground surface

Isotropic inverse-problem approach for two-dimensional phase unwrapping

In this paper, we propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted data-fidelity term that favors sparsity in the error between the true and wrapped phase differences, as well as a regularizer based on higher-order total-variation. One desirable feature of our method is its rotation invariance, which allows it to unwrap a much larger class of images compared to the state of the art. We demonstrate the effectiveness of our method through several experiments on simulated and real data obtained through the tomographic phase microscope. The proposed method can enhance the applicability and outreach of techniques that rely on quantitative phase evaluation

One shot profilometry using iterative two-step temporal phase-unwrapping

This paper reviews two techniques that have been recently published for 3D profilometry and proposes one shot profilometry using iterative two-step temporal phase-unwrapping by combining the composite fringe projection and the iterative two-step temporal phase unwrapping algorithm. In temporal phase unwrapping, many images with different frequency fringe pattern are needed to project which would take much time. In order to solve this problem, Ochoa proposed a phase unwrapping algorithm based on phase partitions using a composite fringe, which only needs projecting one composite fringe pattern with four kinds of frequency information to complete the process of 3D profilometry. However, we found that the fringe order determined through the construction of phase partitions tended to be imprecise. Recently, we proposed an iterative two-step temporal phase unwrapping algorithm, which can achieve high sensitivity and high precision shape measurement. But it needs multiple frames of fringe images which would take much time. In order to take into account both the speed and accuracy of 3D shape measurement, we get a new, and more accurate unwrapping method based on composite fringe pattern by combining these two techniques. This method not only retains the speed advantage of Ochoa's algorithm, but also greatly improves its measurement accuracy. Finally, the experimental evaluation is conducted to prove the validity of the proposed method, and the experimental results show that this method is feasible.Comment: 14 pages, 15 figure

Robust Phase Unwrapping by Convex Optimization

The 2-D phase unwrapping problem aims at retrieving a "phase" image from its modulo $2\pi$ observations. Many applications, such as interferometry or synthetic aperture radar imaging, are concerned by this problem since they proceed by recording complex or modulated data from which a "wrapped" phase is extracted. Although 1-D phase unwrapping is trivial, a challenge remains in higher dimensions to overcome two common problems: noise and discontinuities in the true phase image. In contrast to state-of-the-art techniques, this work aims at simultaneously unwrap and denoise the phase image. We propose a robust convex optimization approach that enforces data fidelity constraints expressed in the corrupted phase derivative domain while promoting a sparse phase prior. The resulting optimization problem is solved by the Chambolle-Pock primal-dual scheme. We show that under different observation noise levels, our approach compares favorably to those that perform the unwrapping and denoising in two separate steps.Comment: 6 pages, 4 figures, submitted in ICIP1