2,089 research outputs found
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
Temporal phase unwrapping using deep learning
The multi-frequency temporal phase unwrapping (MF-TPU) method, as a classical
phase unwrapping algorithm for fringe projection profilometry (FPP), is capable
of eliminating the phase ambiguities even in the presence of surface
discontinuities or spatially isolated objects. For the simplest and most
efficient case, two sets of 3-step phase-shifting fringe patterns are used: the
high-frequency one is for 3D measurement and the unit-frequency one is for
unwrapping the phase obtained from the high-frequency pattern set. The final
measurement precision or sensitivity is determined by the number of fringes
used within the high-frequency pattern, under the precondition that the phase
can be successfully unwrapped without triggering the fringe order error.
Consequently, in order to guarantee a reasonable unwrapping success rate, the
fringe number (or period number) of the high-frequency fringe patterns is
generally restricted to about 16, resulting in limited measurement accuracy. On
the other hand, using additional intermediate sets of fringe patterns can
unwrap the phase with higher frequency, but at the expense of a prolonged
pattern sequence. Inspired by recent successes of deep learning techniques for
computer vision and computational imaging, in this work, we report that the
deep neural networks can learn to perform TPU after appropriate training, as
called deep-learning based temporal phase unwrapping (DL-TPU), which can
substantially improve the unwrapping reliability compared with MF-TPU even in
the presence of different types of error sources, e.g., intensity noise, low
fringe modulation, and projector nonlinearity. We further experimentally
demonstrate for the first time, to our knowledge, that the high-frequency phase
obtained from 64-period 3-step phase-shifting fringe patterns can be directly
and reliably unwrapped from one unit-frequency phase using DL-TPU
Depth Fields: Extending Light Field Techniques to Time-of-Flight Imaging
A variety of techniques such as light field, structured illumination, and
time-of-flight (TOF) are commonly used for depth acquisition in consumer
imaging, robotics and many other applications. Unfortunately, each technique
suffers from its individual limitations preventing robust depth sensing. In
this paper, we explore the strengths and weaknesses of combining light field
and time-of-flight imaging, particularly the feasibility of an on-chip
implementation as a single hybrid depth sensor. We refer to this combination as
depth field imaging. Depth fields combine light field advantages such as
synthetic aperture refocusing with TOF imaging advantages such as high depth
resolution and coded signal processing to resolve multipath interference. We
show applications including synthesizing virtual apertures for TOF imaging,
improved depth mapping through partial and scattering occluders, and single
frequency TOF phase unwrapping. Utilizing space, angle, and temporal coding,
depth fields can improve depth sensing in the wild and generate new insights
into the dimensions of light's plenoptic function.Comment: 9 pages, 8 figures, Accepted to 3DV 201
Phase Unwrapping and One-Dimensional Sign Problems
Sign problems in path integrals arise when different field configurations
contribute with different signs or phases. Phase unwrapping describes a family
of signal processing techniques in which phase differences between elements of
a time series are integrated to construct non-compact unwrapped phase
differences. By combining phase unwrapping with a cumulant expansion, path
integrals with sign problems arising from phase fluctuations can be
systematically approximated as linear combinations of path integrals without
sign problems. This work explores phase unwrapping in zero-plus-one-dimensional
complex scalar field theory. Results with improved signal-to-noise ratios for
the spectrum of scalar field theory can be obtained from unwrapped phases, but
the size of cumulant expansion truncation errors is found to be undesirably
sensitive to the parameters of the phase unwrapping algorithm employed. It is
argued that this numerical sensitivity arises from discretization artifacts
that become large when phases fluctuate close to singularities of a complex
logarithm in the definition of the unwrapped phase.Comment: 42 pages, 16 figures. Journal versio
Learning-based Single-step Quantitative Susceptibility Mapping Reconstruction Without Brain Extraction
Quantitative susceptibility mapping (QSM) estimates the underlying tissue
magnetic susceptibility from MRI gradient-echo phase signal and typically
requires several processing steps. These steps involve phase unwrapping, brain
volume extraction, background phase removal and solving an ill-posed inverse
problem. The resulting susceptibility map is known to suffer from inaccuracy
near the edges of the brain tissues, in part due to imperfect brain extraction,
edge erosion of the brain tissue and the lack of phase measurement outside the
brain. This inaccuracy has thus hindered the application of QSM for measuring
the susceptibility of tissues near the brain edges, e.g., quantifying cortical
layers and generating superficial venography. To address these challenges, we
propose a learning-based QSM reconstruction method that directly estimates the
magnetic susceptibility from total phase images without the need for brain
extraction and background phase removal, referred to as autoQSM. The neural
network has a modified U-net structure and is trained using QSM maps computed
by a two-step QSM method. 209 healthy subjects with ages ranging from 11 to 82
years were employed for patch-wise network training. The network was validated
on data dissimilar to the training data, e.g. in vivo mouse brain data and
brains with lesions, which suggests that the network has generalized and
learned the underlying mathematical relationship between magnetic field
perturbation and magnetic susceptibility. AutoQSM was able to recover magnetic
susceptibility of anatomical structures near the edges of the brain including
the veins covering the cortical surface, spinal cord and nerve tracts near the
mouse brain boundaries. The advantages of high-quality maps, no need for brain
volume extraction and high reconstruction speed demonstrate its potential for
future applications.Comment: 26 page
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Coil combination using linear deconvolution in k-space for phase imaging
Background: The combination of multi-channel data is a critical step for the imaging of phase and susceptibility contrast in magnetic resonance imaging (MRI). Magnitude-weighted phase combination methods often produce noise and aliasing artifacts in the magnitude images at accelerated imaging sceneries. To address this issue, an optimal coil combination method through deconvolution in k-space is proposed in this paper.
Methods: The proposed method firstly employs the sum-of-squares and phase aligning method to yield a complex reference coil image which is then used to calculate the coil sensitivity and its Fourier transform. Then, the coil k-space combining weights is computed, taking into account the truncated frequency data of coil sensitivity and the acquired k-space data. Finally, combining the coil k-space data with the acquired weights generates the k-space data of proton distribution, with which both phase and magnitude information can be obtained straightforwardly. Both phantom and in vivo imaging experiments were conducted to evaluate the performance of the proposed method.
Results: Compared with magnitude-weighted method and MCPC-C, the proposed method can alleviate the phase cancellation in coil combination, resulting in a less wrapped phase.
Conclusions: The proposed method provides an effective and efficient approach to combine multiple coil image in parallel MRI reconstruction, and has potential to benefit routine clinical practice in the future
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