Total-variation (TV)-based Computed Tomography (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 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 consider the use of two accelerated
gradient-based methods, GPBB and UPN, for reducing the number of gradient
method iterations needed to achieve a high-accuracy TV solution 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.Comment: 4 pages, 2 figure
