A General Formula for Fan-Beam Lambda Tomography

Lambda tomography (LT) is to reconstruct a gradient-like image of an object only from local projection data. It is potentially an important technology for medical X-ray computed tomography (CT) at a reduced radiation dose. In this paper, we prove the first general formula for exact and efficient fan-beam LT from data collected along any smooth curve based on even and odd data extensions. As a result, an LT image can be reconstructed without involving any data extension. This implies that structures outside a scanning trajectory do not affect the exact reconstruction of points inside the trajectory even if the data may be measured through the outside features. The algorithm is simulated in a collinear coordinate system. The results support our theoretical analysis.

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Deep learning based adaptive filtering for projection data noise reduction in x-ray computed tomography

15th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine ◽

10.1117/12.2534838 ◽

2019 ◽

Author(s):

Tzu-Cheng Lee ◽

Jian Zhou ◽

Zhou Yu

Keyword(s):

Computed Tomography ◽

Deep Learning ◽

Noise Reduction ◽

Adaptive Filtering ◽

Projection Data ◽

Data Noise ◽

X Ray ◽

X Ray Computed

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Level-set reconstruction algorithm for ultrafast limited-angle X-ray computed tomography of two-phase flows

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2014.0395 ◽

2015 ◽

Vol 373 (2043) ◽

pp. 20140395 ◽

Cited By ~ 3

Author(s):

M. Bieberle ◽

U. Hampel

Keyword(s):

Computed Tomography ◽

Level Set ◽

Reconstruction Algorithm ◽

Projection Data ◽

Reconstruction Technique ◽

Two Phase Flows ◽

Two Phase ◽

X Ray ◽

X Ray Computed ◽

Limited Angle

Tomographic image reconstruction is based on recovering an object distribution from its projections, which have been acquired from all angular views around the object. If the angular range is limited to less than 180° of parallel projections, typical reconstruction artefacts arise when using standard algorithms. To compensate for this, specialized algorithms using a priori information about the object need to be applied. The application behind this work is ultrafast limited-angle X-ray computed tomography of two-phase flows. Here, only a binary distribution of the two phases needs to be reconstructed, which reduces the complexity of the inverse problem. To solve it, a new reconstruction algorithm (LSR) based on the level-set method is proposed. It includes one force function term accounting for matching the projection data and one incorporating a curvature-dependent smoothing of the phase boundary. The algorithm has been validated using simulated as well as measured projections of known structures, and its performance has been compared to the algebraic reconstruction technique and a binary derivative of it. The validation as well as the application of the level-set reconstruction on a dynamic two-phase flow demonstrated its applicability and its advantages over other reconstruction algorithms.

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