Phase-unwrapping algorithm for images with high noise content based on a local histogram

We present a robust algorithm of phase unwrapping that was designed for use on phase images with high noise content. We proceed with the algorithm by first identifying regions with continuous phase values placed between fringe boundaries in an image and then phase shifting the regions with respect to one another by multiples of 2pi to unwrap the phase. Image pixels are segmented between interfringe and fringe boundary areas by use of a local histogram of a wrapped phase. The algorithm has been used successfully to unwrap phase images generated in a three-dimensional shape measurement for noninvasive quantification of human skin structure in dermatology, cosmetology, and plastic surgery.     

Robust brain MRI denoising and segmentation using enhanced non‐local means algorithm

Image denoising is an integral component of many practical medical systems. Non‐local means (NLM) is an effective method for image denoising which exploits the inherent structural redundancy present in images. Improved adaptive non‐local means (IANLM) is an improved variant of classical NLM based on a robust threshold criterion. In this paper, we have proposed an enhanced non‐local means (ENLM) algorithm, for application to brain MRI, by introducing several extensions to the IANLM algorithm. First, a Rician bias correction method is applied for adapting the IANLM algorithm to Rician noise in MR images. Second, a selective median filtering procedure based on fuzzy c‐means algorithm is proposed as a postprocessing step, in order to further improve the quality of IANLM‐filtered image. Third, different parameters of the proposed ENLM algorithm are optimized for application to brain MR images. Different variants of the proposed algorithm have been presented in order to investigate the influence of the proposed modifications. The proposed variants have been validated on both T1‐weighted (T1‐w) and T2‐weighted (T2‐w) simulated and real brain MRI. Compared with other denoising methods, superior quantitative and qualitative denoising results have been obtained for the proposed algorithm. Additionally, the proposed algorithm has been applied to T2‐weighted brain MRI with multiple sclerosis lesion to show its superior capability of preserving pathologically significant information. Finally, impact of the proposed algorithm has been tested on segmentation of brain MRI. Quantitative and qualitative segmentation results verify that the proposed algorithm based segmentation is better compared with segmentation produced by other contemporary techniques.     

Network approaches to two-dimensional phase unwrapping: intractability and two new algorithms

Two-dimensional (2-D) phase unwrapping, that is, deducing unambiguous phase values from a 2-D array of values known only modulo 2pi, is a key step in interpreting data acquired with synthetic aperture radar interferometry. Noting the recent network formulation of the phase unwrapping problem, we apply here some well-established ideas of network theory to formalize the problem, analyze its complexity, and derive algorithms for its solution. It has been suggested that the objective of phase unwrapping should be to minimize the total number of places where unwrapped and wrapped phase gradients differ. Here we use network constructions to show that this so-called minimum L0-norm problem is NP-hard, or one that complexity theory suggests is impossible for efficient algorithms to solve exactly. Therefore we must instead find approximate solutions; we present two new algorithms for doing so. The first uses the network ideas of shortest paths and spanning trees to improve on the Goldstein et al. residue-cut algorithm [Radio Sci. 23, 713 (1988)]. Our improved algorithm is very fast, provides complete coverage, and allows user-defined weights. With our second algorithm, we extend the ideas of linear network flow problems to the nonlinear L0 case. This algorithm yields excellent approximations to the minimum L0 norm. Using interferometric data, we demonstrate that our algorithms are highly competitive with other existing algorithms in speed and accuracy, outperforming them in the cases presented here.     

Highly sensitive wave-front sensor with a non-zero-order phase plate

We propose a novel highly sensitive wave front detection method for a quick check of a flat wave front by taking advantage of a non-zero-order pi phase plate that yields a non-zero-order diffraction pattern. When a light beam with a flat wave front illuminates a phase plate, the zero-order intensity is zero. When there is a slight distortion of the wave front, the zero-order intensity increases. The ratio of first-order intensity to that of zero-order intensity is used as the criterion with which to judge whether the wave front under test is flat, eliminating the influence of background light. Experimental results demonstrate that this method is efficient, robust, and cost-effective and should be highly interesting for a quick check of a flat wave front of a large-aperture laser beam and adaptive optical systems.     

Temporal phase unwrapping and its application in shearography systems

Temporal phase unwrapping is applied to a two-camera polarization phase-stepped system. A simple algorithm for the phase-change calculation is given, together with simulations, to indicate its validity and strength. This method can be applied directly for detection of phase changes as a function of time. It is proposed to use this method in a shearography setup. The phase distribution in the shearogram can then be obtained, without the standard 2pi ambiguities, by application of the required total shear in a number of smaller steps, provided that each step is small enough to be free from these 2pi phase steps.     

Extending the dynamic range of phase contrast magnetic resonance velocity imaging using advanced higher-dimensional phase unwrapping algorithms.

Phase contrast magnetic resonance velocity imaging is a powerful technique for quantitative in vivo blood flow measurement. Current practice normally involves restricting the sensitivity of the technique so as to avoid the problem of the measured phase being 'wrapped' onto the range -pi to +pi. However, as a result, dynamic range and signal-to-noise ratio are sacrificed. Alternatively, the true phase values can be estimated by a phase unwrapping process which consists of adding integral multiples of 2pi to the measured wrapped phase values. In the presence of noise and data undersampling, the phase unwrapping problem becomes non-trivial. In this paper, we investigate the performance of three different phase unwrapping algorithms when applied to three-dimensional (two spatial axes and one time axis) phase contrast datasets. A simple one-dimensional temporal unwrapping algorithm, a more complex and robust three-dimensional unwrapping algorithm and a novel velocity encoding unwrapping algorithm which involves unwrapping along a fourth dimension (the 'velocity encoding' direction) are discussed, and results from the three are presented and compared. It is shown that compared to the traditional approach, both dynamic range and signal-to-noise ratio can be increased by a factor of up to five times, which demonstrates considerable promise for a possible eventual clinical implementation. The results are also of direct relevance to users of any other technique delivering time-varying two-dimensional phase images, such as dynamic speckle interferometry and synthetic aperture radar.     

Modulo 2pi fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm

The fringe orientation angle provides useful information for many fringe-pattern-processing techniques. From a single normalized fringe pattern (background suppressed and modulation normalized), the fringe orientation angle can be obtained by computing the irradiance gradient and performing a further arctangent computation. Because of the 180 degrees ambiguity of the fringe direction, the orientation angle computed from the gradient of a single fringe pattern can be determined only modulo pi. Recently, several studies have shown that a reliable determination of the fringe orientation angle modulo 2pi is a key point for a robust demodulation of the phase from a single fringe pattern. We present an algorithm for the computation of the modulo 2pi fringe orientation angle by unwrapping the orientation angle obtained from the gradient computation with a regularized phase tracking method. Simulated as well as experimental results are presented.     

An adaptive method based on the improved LPA-ICI algorithm for MRI enhancement

Various diseases are diagnosed using medical imaging used for analysing internal anatomical structures. However, medical images are susceptible to noise introduced in both acquisition and transmission processes. We propose an adaptive data-driven image denoising algorithm based on an improvement of the intersection of confidence intervals (ICI), called relative ICI (RICI) algorithm. The 2D mask of the adaptive size and shape is calculated for each image pixel independently, and utilized in the design of the 2D local polynomial approximation (LPA) filters. Denoising performances, in terms of the PSNR, are compared to the original ICI-based method, as well as to the fixed sized filtering. The proposed adaptive RICI-based denoising outperformed the original ICI-based method by up to 1.32 dB, and the fixed size filtering by up to 6.48 dB. Furthermore, since the denoising of each image pixel is done locally and independently, the method is easy to parallelize.     

Evaluation of a preconditioned conjugate-gradient algorithm for weighted least-squares unwrapping of digital speckle-pattern interferometry phase maps

Inasmuch as current fringe analysis techniques used in digital speckle-pattern interferometry (DSPI) yield a phase map modulo 2pi, phase unwrapping is the final step of any data evaluation process. The performance of a recently published algorithm used to unwrap DSPI phase maps is investigated. The algorithm is based on a least-squares minimization technique that is solvable by the discrete cosine transform. When phase inconsistencies are present, they are handled by exclusion of invalid pixels from the unwrapping process through the assignment of zero-valued weights. Then the weighted unwrapping problem is solved in an iterative manner by a preconditioned conjugate-gradient method. The evaluation is carried out with computer-simulated DSPI phase maps, an approach that permits the generation of phase fields without inconsistencies, which are then used to calculate phase deviations as a function of the iteration number. Real data are also used to illustrate the performance of the algorithm.     

Denoising quadrature Doppler signals from bi-directional flow using the wavelet frame

A novel approach was proposed to denoise quadrature Doppler signals from bi-directional blood flow using the wavelet frame and a soft-thresholding algorithm. A direction separation step was carried out first to avoid the phase distortion of quadrature Doppler signals, which is induced from the nonlinear, soft-thresholding processing. Then real parts of separated complex signals from the unidirectional flow were denoised independently. The quadrature Doppler signals from the bi-directional flow were reconstructed from the denoised separated signals. The approach has been applied to the simulated Doppler signals from a femoral artery. It is concluded from the experimental results that this method is practical for denoising quadrature Doppler signals.     

Two-dimensional phase unwrapping using a hybrid genetic algorithm

A novel hybrid genetic algorithm (HGA) is proposed to solve the branch-cut phase unwrapping problem. It employs both local and global search methods. The local search is implemented by using the nearest-neighbor method, whereas the global search is performed by using the genetic algorithm. The branch-cut phase unwrapping problem [a nondeterministic polynomial (NP-hard) problem] is implemented in a similar way to the traveling-salesman problem, a very-well-known combinational optimization problem with profound research and applications. The performance of the proposed algorithm was tested on both simulated and real wrapped phase maps. The HGA is found to be robust and fast compared with three well-known branch-cut phase unwrapping algorithms.     

Full-field automated photoelasticity by fourier polarimetry with three wavelengths

The search for fast, precise, and robust testing techniques remains an important problem in automated full-field photoelasticity. The polarizer-sample-analyzer (PSA)-based three-wavelength polarimetric method presented here employs discrete Fourier analysis and a spectral content unwrapping algorithm to provide completely automatic, simple, fast, and accurate determination of both photoelastic parameters. Fourier analysis of experimental data and a three-wavelength approach reduce the effect of noise and efficiently cope with poor accuracy in regions of both isochromatic and isoclinic maps. Because any polarimetric technique yields the phase value in the principal range of the corresponding trigonometric function, the final step in data processing is phase unwrapping. Because of the good quality of the wrapped phase map and because each point is processed independently, our suggested three-wavelength unwrapping algorithm exhibits a high level of robustness. Unlike some other PSA three-wavelength techniques, the given algorithm here solves the problem of phase unwrapping completely. Specifically, it converts experimentally obtained arccosine-type phase maps directly into full phase value distributions, skipping the step of generating an arctangent-type ramped phase map and resorting to other unwrapping routines for final data processing. The accuracy of the new technique has been estimated with a Babinet-Soleil compensator. Test experiments with the disk in diametric compression and a quartz plate have proved that the technique can be used for precise determination of the isoclinic angle and relative retardation, even for large values of the latter.     

Recycling of solution spaces in multipreconditioned FETI methods applied to structural dynamics

This article presents a new method to recycle the solution space of an adaptive multipreconditioned finite element tearing and interconnecting algorithm in the case where the same operator is solved for multiple right‐hand sides like in linear structural dynamics. It accelerates the computation from the second time step on by applying a coarse space that is generated from Ritz approximations of local eigenproblems, using the solution space of the first time step. These eigenproblems are known to provide very efficient coarse spaces but must usually be solved a priori at high computational cost. Their Ritz approximations are much smaller and less expensive to solve. Recycling methods based on Ritz approximations of global eigenproblems have been published for classical finite element tearing and interconnecting algorithms, but their efficient application to multipreconditioned variants is not possible. This article also presents the application of a simpler recycling procedure, which reuses plain solution spaces, to adaptive multipreconditioned finite element tearing and interconnecting. Numerical results of the application of the presented methods to four test cases are shown. The new Ritz approximation method leads to coarse spaces, which turn out to be as efficient as those obtained from solving the unreduced eigenproblems. It is the most efficient recycling method currently available for multipreconditioned dual domain decomposition techniques.     

Unwrapping of interferometric phase-fringe maps by the discrete cosine transform

Current whole-field interferometric techniques yield a phase distribution in modulo 2π. Removal of the resulting cyclic discontinuities is a process known as unwrapping, which must be performed before the data can be interpreted. We investigate an iterative unwrapping technique recently published by Ghiglia and Romero [J. Opt. Soc. Am. A 11, 107 (1994)], which is based on least-squares minimization, obtained by the discrete cosine transform. We apply this technique to remove phase wraps from electronic speckle pattern interferometry data, using modest personal computer hardware. The algorithm is shown to be fast, easy to implement, robust in the presence of noise, and able to handle phase inconsistencies without propagating local errors.     

EM algorithm‐based adaptive custom thresholding for image denoising in wavelet domain

In this article, a novel denoising technique based on custom thresholding operating in the wavelet transform domain is proposed. The denoising process is spatially adaptive and also sub‐band adaptive. To render the denoising algorithm space adaptive, a Vector Quantization (VQ)‐based algorithm is used. The design of the VQ is based on Expectation Maximization (EM) algorithm. The results of the algorithm is demonstrated on SAR images corrupted by speckle noise. Experimental results show that Custom thresholding function outperforms the traditional soft, hard, and Bayes threshoding functions, improving the denoised results significantly in terms of Peak Signal to Noise Ratio (PSNR). © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 175–178, 2009     

Phase reconstruction from undersampled intensity patterns

We demonstrate the uniqueness and convergence of phase recovery from high-spatial-frequency and undersampled intensity data. Furthermore, this is accomplished without the ambiguities that arise in phase unwrapping and without the need to employ a priori information. The method incorporates the technique of line integration of the phase gradient to find the first approximation to the phase and the algorithm of synthetic interferograms to find the unknown phase with high accuracy. The method may be used with any experimental method that at a certain data processing step obtains generalized sine and cosine intensity functions.     

Phase-slope and group-dispersion calculations in the frequency domain by simple optical low-coherence reflectometry

We report a new method by which phase slope and group dispersion can be calculated with a simple optical low-coherence reflectometer to quantify physiological conditions. A discrete-time signal processing algorithm based on the first and second derivatives of the phase with respect to wave number was developed from discrete-time Fourier properties. The algorithm avoids the 2pi ambiguity associated with most phase unwrapping. Experimental data collected by use of well-characterized optical materials validated the algorithm, which was minimally sensitive to phase noise. The group dispersion of bovine cornea was measured at various hydrations and was significantly dependent on hydration. The results suggest that group dispersion is an indicator of corneal alterations.     

Fast and robust three-dimensional best path phase unwrapping algorithm

What we believe to be a novel three-dimensional (3D) phase unwrapping algorithm is proposed to unwrap 3D wrapped-phase volumes. It depends on a quality map to unwrap the most reliable voxels first and the least reliable voxels last. The technique follows a discrete unwrapping path to perform the unwrapping process. The performance of this technique was tested on both simulated and real wrapped-phase maps. And it is found to be robust and fast compared with other 3D phase unwrapping algorithms.     

Effect of phase mismatch on pseudo-phase-step analysis of time-average hologram recordings of vibration modes

I present the results of an experiment to demonstrate the effect of phase mismatch between an object vibration and a bias vibration in pseudo-phase-step analysis of time-average holographic interferograms of vibration modes. Pseudo-phase-stepping applies conventional phase-step equations to zero-order Bessel function fringes and during phase unwrapping corrects for the errors incurred. A circular disk vibrating in a quadrature combination of its two one-diameter modes was used as a test object and provided a 360 degrees phase distribution. The results indicate that the process has considerable tolerance to phase mismatch.