87 research outputs found
Artifacts in incomplete data tomography - with applications to photoacoustic tomography and sonar
We develop a paradigm using microlocal analysis that allows one to
characterize the visible and added singularities in a broad range of incomplete
data tomography problems. We give precise characterizations for photo- and
thermoacoustic tomography and Sonar, and provide artifact reduction strategies.
In particular, our theorems show that it is better to arrange Sonar detectors
so that the boundary of the set of detectors does not have corners and is
smooth. To illustrate our results, we provide reconstructions from synthetic
spherical mean data as well as from experimental photoacoustic data
On Artifacts in Limited Data Spherical Radon Transform: Curved Observation Surface
In this article, we consider the limited data problem for spherical mean
transform. We characterize the generation and strength of the artifacts in a
reconstruction formula. In contrast to the third's author work [Ngu15b], the
observation surface considered in this article is not flat. Our results are
comparable to those obtained in [Ngu15b] for flat observation surface. For the
two dimensional problem, we show that the artifacts are orders smoother
than the original singularities, where is vanishing order of the smoothing
function. Moreover, if the original singularity is conormal, then the artifacts
are order smoother than the original singularity. We provide
some numerical examples and discuss how the smoothing effects the artifacts
visually. For three dimensional case, although the result is similar to that
[Ngu15b], the proof is significantly different. We introduce a new idea of
lifting the space
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
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