A reconstruction method for equidistant fan beam differential phase contrast computed tomography

Fu, Jian; Li, Peng; Wang, Q L; Wang, S Y; Bech, Martin; Tapfer, Arne; Hahn, D; Pfeiffer, Franz

doi:10.1088/0031-9155/56/14/019

Cited by 17 publications

(8 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For fan-beam projection data on a flat panel detector array (Figure 1(b)), Fu provided a back-projection filtration (BPF) algorithm to reconstruct the 2-D image 24 . This BPF algorithm is expressed as…”

Section: Methodsmentioning

confidence: 99%

Interior tomography from differential phase contrast data via Hilbert transform based on spline functions

2016

View full text Add to dashboard Cite

X-ray phase contrast imaging is an important mode due to its sensitivity to subtle features of soft biological tissues. Grating-based differential phase contrast (DPC) imaging is one of the most promising phase imaging techniques because it works with a normal x-ray tube of a large focal spot at a high flux rate. However, a main obstacle before this paradigm shift is the fabrication of large-area gratings of a small period and a high aspect ratio. Imaging large objects with a size-limited grating results in data truncation which is a new type of the interior problem. While the interior problem was solved for conventional x-ray CT through analytic extension, compressed sensing and iterative reconstruction, the difficulty for interior reconstruction from DPC data lies in that the implementation of the system matrix requires the differential operation on the detector array, which is often inaccurate and unstable in the case of noisy data. Here, we propose an iterative method based on spline functions. The differential data are first back-projected to the image space. Then, a system matrix is calculated whose components are the Hilbert transforms of the spline bases. The system matrix takes the whole image as an input and outputs the back-projected interior data. Prior information normally assumed for compressed sensing is enforced to iteratively solve this inverse problem. Our results demonstrate that the proposed algorithm can successfully reconstruct an interior region of interest (ROI) from the differential phase data through the ROI.

show abstract

Section: Methodsmentioning

confidence: 99%

Interior tomography from differential phase contrast data via Hilbert transform based on spline functions

2016

View full text Add to dashboard Cite

show abstract

“…It has been developed to get the phase shift cross section tomographic image of the samples. Over the last years, several PC-CT methods have been developed [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Most of them are based on analyzer and grating or free propagation theory [23].…”

Section: Introductionmentioning

confidence: 99%

In-line phase contrast micro-CT reconstruction for biomedical specimens

Tan

2014

Bio-Medical Materials and Engineering

View full text Add to dashboard Cite

X-ray phase contrast micro computed tomography (micro-CT) can non-destructively provide the internal structure information of soft tissues and low atomic number materials. It has become an invaluable analysis tool for biomedical specimens. Here an in-line phase contrast micro-CT reconstruction technique is reported, which consists of a projection extraction method and the conventional filter back-projection (FBP) reconstruction algorithm. The projection extraction is implemented by applying the Fourier transform to the forward projections of in-line phase contrast micro-CT. This work comprises a numerical study of the method and its experimental verification using a biomedical specimen dataset measured at an X-ray tube source micro-CT setup. The numerical and experimental results demonstrate that the presented technique can improve the imaging contrast of biomedical specimens. It will be of interest for a wide range of in-line phase contrast micro-CT applications in medicine and biology.

show abstract

“…The references [27,57,58] are reconstruction algorithms in Fourier domain. The references [29,30,32,41,50,52,53,55,63] are reconstruction algorithms with FBP method. The references [36,47,48] are reconstruction algorithms with total variation (TV) minimization or compressed sensing method.…”

Section: Introductionmentioning

confidence: 99%

Fan beam image reconstruction with generalized fourier slice theorem

Zhao¹,

Yang²,

Yang³

2014

Journal of X-Ray Science and Technology

View full text Add to dashboard Cite

For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data.(2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N 3 ), where N is the number of pixel in one dimension.

show abstract

A reconstruction method for equidistant fan beam differential phase contrast computed tomography

Cited by 17 publications

References 33 publications

Interior tomography from differential phase contrast data via Hilbert transform based on spline functions

Interior tomography from differential phase contrast data via Hilbert transform based on spline functions

In-line phase contrast micro-CT reconstruction for biomedical specimens

Fan beam image reconstruction with generalized fourier slice theorem

Contact Info

Product

Resources

About