49,456 research outputs found
3D particle tracking velocimetry using dynamic discrete tomography
Particle tracking velocimetry in 3D is becoming an increasingly important
imaging tool in the study of fluid dynamics, combustion as well as plasmas. We
introduce a dynamic discrete tomography algorithm for reconstructing particle
trajectories from projections. The algorithm is efficient for data from two
projection directions and exact in the sense that it finds a solution
consistent with the experimental data. Non-uniqueness of solutions can be
detected and solutions can be tracked individually
Dynamic discrete tomography
We consider the problem of reconstructing the paths of a set of points over
time, where, at each of a finite set of moments in time the current positions
of points in space are only accessible through some small number of their
X-rays. This particular particle tracking problem, with applications, e.g., in
plasma physics, is the basic problem in dynamic discrete tomography. We
introduce and analyze various different algorithmic models. In particular, we
determine the computational complexity of the problem (and various of its
relatives) and derive algorithms that can be used in practice. As a byproduct
we provide new results on constrained variants of min-cost flow and matching
problems.Comment: In Pres
Multiple Projection Optical Diffusion Tomography with Plane Wave Illumination
We describe a new data collection scheme for optical diffusion tomography in
which plane wave illumination is combined with multiple projections in the slab
imaging geometry. Multiple projection measurements are performed by rotating
the slab around the sample. The advantage of the proposed method is that the
measured data can be much more easily fitted into the dynamic range of most
commonly used detectors. At the same time, multiple projections improve image
quality by mutually interchanging the depth and transverse directions, and the
scanned (detection) and integrated (illumination) surfaces. Inversion methods
are derived for image reconstructions with extremely large data sets. Numerical
simulations are performed for fixed and rotated slabs
Accelerated High-Resolution Photoacoustic Tomography via Compressed Sensing
Current 3D photoacoustic tomography (PAT) systems offer either high image
quality or high frame rates but are not able to deliver high spatial and
temporal resolution simultaneously, which limits their ability to image dynamic
processes in living tissue. A particular example is the planar Fabry-Perot (FP)
scanner, which yields high-resolution images but takes several minutes to
sequentially map the photoacoustic field on the sensor plane, point-by-point.
However, as the spatio-temporal complexity of many absorbing tissue structures
is rather low, the data recorded in such a conventional, regularly sampled
fashion is often highly redundant. We demonstrate that combining variational
image reconstruction methods using spatial sparsity constraints with the
development of novel PAT acquisition systems capable of sub-sampling the
acoustic wave field can dramatically increase the acquisition speed while
maintaining a good spatial resolution: First, we describe and model two general
spatial sub-sampling schemes. Then, we discuss how to implement them using the
FP scanner and demonstrate the potential of these novel compressed sensing PAT
devices through simulated data from a realistic numerical phantom and through
measured data from a dynamic experimental phantom as well as from in-vivo
experiments. Our results show that images with good spatial resolution and
contrast can be obtained from highly sub-sampled PAT data if variational image
reconstruction methods that describe the tissues structures with suitable
sparsity-constraints are used. In particular, we examine the use of total
variation regularization enhanced by Bregman iterations. These novel
reconstruction strategies offer new opportunities to dramatically increase the
acquisition speed of PAT scanners that employ point-by-point sequential
scanning as well as reducing the channel count of parallelized schemes that use
detector arrays.Comment: submitted to "Physics in Medicine and Biology
A Novel Convex Relaxation for Non-Binary Discrete Tomography
We present a novel convex relaxation and a corresponding inference algorithm
for the non-binary discrete tomography problem, that is, reconstructing
discrete-valued images from few linear measurements. In contrast to state of
the art approaches that split the problem into a continuous reconstruction
problem for the linear measurement constraints and a discrete labeling problem
to enforce discrete-valued reconstructions, we propose a joint formulation that
addresses both problems simultaneously, resulting in a tighter convex
relaxation. For this purpose a constrained graphical model is set up and
evaluated using a novel relaxation optimized by dual decomposition. We evaluate
our approach experimentally and show superior solutions both mathematically
(tighter relaxation) and experimentally in comparison to previously proposed
relaxations
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