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Transform‐domain penalized‐likelihood filtering of tomographic data
Author(s) -
Atkinson Ian C.,
Kamalabadi Farzad
Publication year - 2008
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/ima.20171
Subject(s) - regularization (linguistics) , radon transform , projection (relational algebra) , algorithm , dimension (graph theory) , filter (signal processing) , computer science , mathematics , domain (mathematical analysis) , tomographic reconstruction , artificial intelligence , iterative reconstruction , computer vision , mathematical analysis , pure mathematics
We present motivation for performing the filtering step of the widely used filtered back‐projection algorithm in a non‐Radon domain. For square‐error optimal penalized‐likelihood regularization, filtering in a domain for which the true projection data is sparse in the angle dimension yields coefficients that are more faithful to the ideal filtered data than directly filtering the observed Radon‐domain data. In contrast to traditional regularization techniques that filter each projection independently, the proposed filtering technique delivers improved reconstructions by exploiting the correlation of the data in the angle dimension. This enables meaningful reconstructions to be created even from very noisy projection data. In addition, this approach allows for simple penalty matrices to be constructed, enables penalty coefficient to be calculated in a straightforward manner, and results in an easily computed, closed‐form solution for the regularizing filters. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 18, 350–364, 2008