Abstract
Total-variation (TV)-based CT image reconstruction
has shown experimentally to be capable of producing accurate
reconstructions from sparse-view data. In particular TV-based
reconstruction is very well suited for images with piecewise
nearly constant regions. Computationally, however, TV-based reconstruction
is much more demanding, especially for 3D imaging,
and the reconstruction from clinical data sets is far from being
close to real-time. This is undesirable from a clinical perspective,
and thus there is an incentive to accelerate the solution of the
underlying optimization problem.
The TV reconstruction can in principle be found by any
optimization method, but in practice the large scale of the
systems arising in CT image reconstruction preclude the use
of memory-demanding methods such as Newton’s method. The
simple gradient method has much lower memory requirements,
but exhibits slow convergence.
In the present work we address the question of how to reduce
the number of gradient method iterations needed to achieve a
high-accuracy TV reconstruction. We consider the use of two
accelerated gradient-based methods, GPBB and UPN, to solve
the 3D-TV minimization problem in CT image reconstruction.
The former incorporates several heuristics from the optimization
literature such as Barzilai-Borwein (BB) step size selection and
nonmonotone line search. The latter uses a cleverly chosen
sequence of auxiliary points to achieve a better convergence rate.
The methods are memory efficient and equipped with a
stopping criterion to ensure that the TV reconstruction has
indeed been found. An implementation of the methods (in
C with interface to Matlab) is available for download from
http://www2.imm.dtu.dk/pch/TVReg/.
We compare the proposed methods with the standard gradient
method, applied to a 3D test problem with synthetic few-view
data. We find experimentally that for realistic parameters the
proposed methods significantly outperform the gradient method.
Original language | English |
---|---|
Title of host publication | Proceedings of 11th Fully 3D Meeting |
Publication date | 2011 |
Publication status | Published - 2011 |
Event | 11th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine - Potsdam, Germany Duration: 11 Jul 2011 → 15 Jul 2011 Conference number: 11 http://www.fully3d.org/2011/index.html |
Conference
Conference | 11th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine |
---|---|
Number | 11 |
Country/Territory | Germany |
City | Potsdam |
Period | 11/07/2011 → 15/07/2011 |
Internet address |