Unwrapped Phase Map Research Articles

A model-based method for phase unwrapping

Presents a model-based phase unwrapping method which represents the unwrapped phase function by a truncated Taylor series and a residual function. An efficient, noniterative computational algorithm is also proposed for calculating the model parameters from the phase derivatives. Sample experimental results are shown to demonstrate the effectiveness of the algorithm for extracting unwrapped phase images from two-dimensional (2-D) magnetic resonance imaging (MRI) data.

Processing of interferometric phase maps as complex-valued phasor images

Phase and amplitude information obtained from phase-shifting interferometry may be combined, to be a complex-valued phasor for every pixel of the image. Phasor image processing is presented as a simple yet effective concept for filtering, visualization, masking, and unwrapping interferometric phase maps. The results from two electronic speckle pattern interferometry data sets illustrate the new method.

Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm

An algorithm for unwrapping noisy phase maps by means of branch cuts has been proposed recently. These cuts join discontinuity sources that mark the beginning or end of a 2π phase discontinuity. After the placement of branch cuts, the unwrapped phase map is unique and independent of the unwrapping route. We show how a minimum-cost-matching graph-theory method can be used to find the set of cuts that has the global minimum of total cut length, in time approximately proportional to the square of the number of sources. The method enables one to unwrap unfiltered speckle-interferometry phase maps at higher source densities (0.1 sources pixel(-1)) than any previous branch-cut placement algorithm.

Temporal phase-unwrapping algorithm for automated interferogram analysis

A new algorithm is proposed for unwrapping interferometric phase maps. Existing algorithms search the two-dimensional spatial domain for 2π discontinuities: only one phase map is required, but phase errors can propagate outward from regions of high noise, corrupting the rest of the image. An alternative approach based on one-dimensional unwrapping along the time axis is proposed. It is applicable to an important subclass of interferometry applications, in which a sequence of incremental phase maps can be obtained leading up to the final phase-difference map of interest. A particular example is quasi-static deformation analysis. The main advantages are (i) it is inherently simple, (ii) phase errors are constrained within the high-noise regions, and (iii) phase maps containing global discontinuities are unwrapped correctly, provided the positions of the discontinuities remain fixed with time. The possibility of real-time phase unwrapping is also discussed.

Spectroscopic imaging by quadrature modulated echo time shifting

To incorporate a novel imaging sequence for robust air and tissue segmentation using ultrashort echo time (UTE) phase images and to implement an innovative synthetic CT (synCT) solution as a first step toward MR-only radiation therapy treatment planning for brain cancer.Ten brain cancer patients were scanned with a UTE/Dixon sequence and other clinical sequences on a 1.0 T open magnet with simulation capabilities. Bone-enhanced images were generated from a weighted combination of water/fat maps derived from Dixon images and inverted UTE images. Automated air segmentation was performed using unwrapped UTE phase maps. Segmentation accuracy was assessed by calculating segmentation errors (true-positive rate, false-positive rate, and Dice similarity indices using CT simulation (CT-SIM) as ground truth. The synCTs were generated using a voxel-based, weighted summation method incorporating T2, fluid attenuated inversion recovery (FLAIR), UTE1, and bone-enhanced images. Mean absolute error (MAE) characterized Hounsfield unit (HU) differences between synCT and CT-SIM. A dosimetry study was conducted, and differences were quantified using γ-analysis and dose-volume histogram analysis.On average, true-positive rate and false-positive rate for the CT and MR-derived air masks were 80.8% ± 5.5% and 25.7% ± 6.9%, respectively. Dice similarity indices values were 0.78 ± 0.04 (range, 0.70-0.83). Full field of view MAE between synCT and CT-SIM was 147.5 ± 8.3 HU (range, 138.3-166.2 HU), with the largest errors occurring at bone–air interfaces (MAE 422.5 ± 33.4 HU for bone and 294.53 ± 90.56 HU for air). Gamma analysis revealed pass rates of 99.4% ± 0.04%, with acceptable treatment plan quality for the cohort.A hybrid MRI phase/magnitude UTE image processing technique was introduced that significantly improved bone and air contrast in MRI. Segmented air masks and bone-enhanced images were integrated into our synCT pipeline for brain, and results agreed well with clinical CTs, thereby supporting MR-only radiation therapy treatment planning in the brain.

Waveform estimation using group delay processing

A method of signal waveform estimation from an ensemble of jittered noisy measurements is presented. The method uses group delay functions to perform the ensemble averaging and thus overcomes the difficulty of computing the unwrapped phase function before averaging. We propose a new technique, called group delay processing, to estimate the signal waveform if only a single noisy measurement is available. We demonstrate our group delay averaging and group delay processing techniques through illustrative examples.