566 research outputs found
A new steplength selection for scaled gradient methods with application to image deblurring
Gradient methods are frequently used in large scale image deblurring problems
since they avoid the onerous computation of the Hessian matrix of the objective
function. Second order information is typically sought by a clever choice of
the steplength parameter defining the descent direction, as in the case of the
well-known Barzilai and Borwein rules. In a recent paper, a strategy for the
steplength selection approximating the inverse of some eigenvalues of the
Hessian matrix has been proposed for gradient methods applied to unconstrained
minimization problems. In the quadratic case, this approach is based on a
Lanczos process applied every m iterations to the matrix of the most recent m
back gradients but the idea can be extended to a general objective function. In
this paper we extend this rule to the case of scaled gradient projection
methods applied to non-negatively constrained minimization problems, and we
test the effectiveness of the proposed strategy in image deblurring problems in
both the presence and the absence of an explicit edge-preserving regularization
term
On the filtering effect of iterative regularization algorithms for linear least-squares problems
Many real-world applications are addressed through a linear least-squares
problem formulation, whose solution is calculated by means of an iterative
approach. A huge amount of studies has been carried out in the optimization
field to provide the fastest methods for the reconstruction of the solution,
involving choices of adaptive parameters and scaling matrices. However, in
presence of an ill-conditioned model and real data, the need of a regularized
solution instead of the least-squares one changed the point of view in favour
of iterative algorithms able to combine a fast execution with a stable
behaviour with respect to the restoration error. In this paper we want to
analyze some classical and recent gradient approaches for the linear
least-squares problem by looking at their way of filtering the singular values,
showing in particular the effects of scaling matrices and non-negative
constraints in recovering the correct filters of the solution
Rapid deconvolution of low-resolution time-of-flight data using Bayesian inference
The deconvolution of low-resolution time-of-flight data has numerous advantages, including the ability to extract additional information from the experimental data. We augment the well-known Lucy-Richardson deconvolution algorithm using various Bayesian prior distributions and show that a prior of second-differences of the signal outperforms the standard Lucy-Richardson algorithm, accelerating the rate of convergence by more than a factor of four, while preserving the peak amplitude ratios of a similar fraction of the total peaks. A novel stopping criterion and boosting mechanism are implemented to ensure that these methods converge to a similar final entropy and local minima are avoided. Improvement by a factor of two in mass resolution allows more accurate quantification of the spectra. The general method is demonstrated in this paper through the deconvolution of fragmentation peaks of the 2,5-dihydroxybenzoic acid matrix and the benzyltriphenylphosphonium thermometer ion, following femtosecond ultraviolet laser desorption
Post-Reconstruction Deconvolution of PET Images by Total Generalized Variation Regularization
Improving the quality of positron emission tomography (PET) images, affected
by low resolution and high level of noise, is a challenging task in nuclear
medicine and radiotherapy. This work proposes a restoration method, achieved
after tomographic reconstruction of the images and targeting clinical
situations where raw data are often not accessible. Based on inverse problem
methods, our contribution introduces the recently developed total generalized
variation (TGV) norm to regularize PET image deconvolution. Moreover, we
stabilize this procedure with additional image constraints such as positivity
and photometry invariance. A criterion for updating and adjusting automatically
the regularization parameter in case of Poisson noise is also presented.
Experiments are conducted on both synthetic data and real patient images.Comment: First published in the Proceedings of the 23rd European Signal
Processing Conference (EUSIPCO-2015) in 2015, published by EURASI
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