On the numerical implementation of discrete finite Hilbert transform for image reconstruction

2012 ◽  
Author(s):  
Yi Yang ◽  
Shaojie Tang ◽  
Xiangyang Tang
Keyword(s):  
Image Reconstruction ◽  
Hilbert Transform ◽  
Numerical Implementation ◽  
Finite Hilbert Transform

scholarly journals Approximating the finite Hilbert transform via trapezoid type inequalities

2002 ◽  
Vol 43 (10-11) ◽  
pp. 1359-1369 ◽  
Author(s):  
N.M. Dragomir ◽  
S.S. Dragomir ◽  
P. Farrell
Keyword(s):  
Hilbert Transform ◽  
Finite Hilbert Transform

scholarly journals A General Local Reconstruction Approach Based on a Truncated Hilbert Transform

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
Yangbo Ye ◽  
Hengyong Yu ◽  
Yuchuan Wei ◽  
Ge Wang
Keyword(s):  
Image Reconstruction ◽  
Hilbert Transform ◽  
Region Of Interest ◽  
Cone Beam ◽  
Projection Data ◽  
Partial Knowledge ◽  
Practical Applications ◽  
Beam Geometry ◽  
Volume Of Interest ◽  
Simulation Results

Exact image reconstruction from limited projection data has been a central topic in the computed tomography (CT) field. In this paper, we present a general region-of-interest/volume-of-interest (ROI/VOI) reconstruction approach using a truly truncated Hilbert transform on a line-segment inside a compactly supported object aided by partial knowledge on one or both neighboring intervals of that segment. Our approach and associated new data sufficient condition allows the most flexible ROI/VOI image reconstruction from the minimum account of data in both the fan-beam and cone-beam geometry. We also report primary numerical simulation results to demonstrate the correctness and merits of our finding. Our work has major theoretical potentials and innovative practical applications.

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