1,598 research outputs found
Compressive X-ray phase tomography based on the transport of intensity equation
We develop and implement a compressive reconstruction method for tomographic
recovery of refractive index distribution for weakly attenuating objects in a
microfocus X-ray system. This is achieved through the development of a
discretized operator modeling both the transport of intensity equation and
X-ray transform that is suitable for iterative reconstruction techniques
Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm
The primal-dual optimization algorithm developed in Chambolle and Pock (CP),
2011 is applied to various convex optimization problems of interest in computed
tomography (CT) image reconstruction. This algorithm allows for rapid
prototyping of optimization problems for the purpose of designing iterative
image reconstruction algorithms for CT. The primal-dual algorithm is briefly
summarized in the article, and its potential for prototyping is demonstrated by
explicitly deriving CP algorithm instances for many optimization problems
relevant to CT. An example application modeling breast CT with low-intensity
X-ray illumination is presented.Comment: Resubmitted to Physics in Medicine and Biology. Text has been
modified according to referee comments, and typos in the equations have been
correcte
Fast Stochastic Hierarchical Bayesian MAP for Tomographic Imaging
Any image recovery algorithm attempts to achieve the highest quality
reconstruction in a timely manner. The former can be achieved in several ways,
among which are by incorporating Bayesian priors that exploit natural image
tendencies to cue in on relevant phenomena. The Hierarchical Bayesian MAP
(HB-MAP) is one such approach which is known to produce compelling results
albeit at a substantial computational cost. We look to provide further analysis
and insights into what makes the HB-MAP work. While retaining the proficient
nature of HB-MAP's Type-I estimation, we propose a stochastic
approximation-based approach to Type-II estimation. The resulting algorithm,
fast stochastic HB-MAP (fsHBMAP), takes dramatically fewer operations while
retaining high reconstruction quality. We employ our fsHBMAP scheme towards the
problem of tomographic imaging and demonstrate that fsHBMAP furnishes promising
results when compared to many competing methods.Comment: 5 Pages, 4 Figures, Conference (Accepted to Asilomar 2017
Task adapted reconstruction for inverse problems
The paper considers the problem of performing a task defined on a model
parameter that is only observed indirectly through noisy data in an ill-posed
inverse problem. A key aspect is to formalize the steps of reconstruction and
task as appropriate estimators (non-randomized decision rules) in statistical
estimation problems. The implementation makes use of (deep) neural networks to
provide a differentiable parametrization of the family of estimators for both
steps. These networks are combined and jointly trained against suitable
supervised training data in order to minimize a joint differentiable loss
function, resulting in an end-to-end task adapted reconstruction method. The
suggested framework is generic, yet adaptable, with a plug-and-play structure
for adjusting both the inverse problem and the task at hand. More precisely,
the data model (forward operator and statistical model of the noise) associated
with the inverse problem is exchangeable, e.g., by using neural network
architecture given by a learned iterative method. Furthermore, any task that is
encodable as a trainable neural network can be used. The approach is
demonstrated on joint tomographic image reconstruction, classification and
joint tomographic image reconstruction segmentation
Deep learning in computational microscopy
We propose to use deep convolutional neural networks (DCNNs) to perform 2D and 3D computational imaging. Specifically, we investigate three different applications. We first try to solve the 3D inverse scattering problem based on learning a huge number of training target and speckle pairs. We also demonstrate a new DCNN architecture to perform Fourier ptychographic Microscopy (FPM) reconstruction, which achieves high-resolution phase recovery with considerably less data than standard FPM. Finally, we employ DCNN models that can predict focused 2D fluorescent microscopic images from blurred images captured at overfocused or underfocused planes.Published versio
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