694 research outputs found
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
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
Inexact Bregman iteration with an application to Poisson data reconstruction
This work deals with the solution of image restoration problems by an
iterative regularization method based on the Bregman iteration. Any iteration of this
scheme requires to exactly compute the minimizer of a function. However, in some
image reconstruction applications, it is either impossible or extremely expensive to
obtain exact solutions of these subproblems. In this paper, we propose an inexact
version of the iterative procedure, where the inexactness in the inner subproblem
solution is controlled by a criterion that preserves the convergence of the Bregman
iteration and its features in image restoration problems. In particular, the method
allows to obtain accurate reconstructions also when only an overestimation of the
regularization parameter is known. The introduction of the inexactness in the iterative
scheme allows to address image reconstruction problems from data corrupted by
Poisson noise, exploiting the recent advances about specialized algorithms for the
numerical minimization of the generalized KullbackâLeibler divergence combined with
a regularization term. The results of several numerical experiments enable to evaluat
Inverse Problems with Poisson noise: Primal and Primal-Dual Splitting
In this paper, we propose two algorithms for solving linear inverse problems
when the observations are corrupted by Poisson noise. A proper data fidelity
term (log-likelihood) is introduced to reflect the Poisson statistics of the
noise. On the other hand, as a prior, the images to restore are assumed to be
positive and sparsely represented in a dictionary of waveforms. Piecing
together the data fidelity and the prior terms, the solution to the inverse
problem is cast as the minimization of a non-smooth convex functional. We
establish the well-posedness of the optimization problem, characterize the
corresponding minimizers, and solve it by means of primal and primal-dual
proximal splitting algorithms originating from the field of non-smooth convex
optimization theory. Experimental results on deconvolution and comparison to
prior methods are also reported
Linear inverse problems with noise: primal and primal-dual splitting
In this paper, we propose two algorithms for solving linear inverse problems
when the observations are corrupted by noise. A proper data fidelity term
(log-likelihood) is introduced to reflect the statistics of the noise (e.g.
Gaussian, Poisson). On the other hand, as a prior, the images to restore are
assumed to be positive and sparsely represented in a dictionary of waveforms.
Piecing together the data fidelity and the prior terms, the solution to the
inverse problem is cast as the minimization of a non-smooth convex functional.
We establish the well-posedness of the optimization problem, characterize the
corresponding minimizers, and solve it by means of primal and primal-dual
proximal splitting algorithms originating from the field of non-smooth convex
optimization theory. Experimental results on deconvolution, inpainting and
denoising with some comparison to prior methods are also reported
Deconvolution under Poisson noise using exact data fidelity and synthesis or analysis sparsity priors
In this paper, we propose a Bayesian MAP estimator for solving the
deconvolution problems when the observations are corrupted by Poisson noise.
Towards this goal, a proper data fidelity term (log-likelihood) is introduced
to reflect the Poisson statistics of the noise. On the other hand, as a prior,
the images to restore are assumed to be positive and sparsely represented in a
dictionary of waveforms such as wavelets or curvelets. Both analysis and
synthesis-type sparsity priors are considered. Piecing together the data
fidelity and the prior terms, the deconvolution problem boils down to the
minimization of non-smooth convex functionals (for each prior). We establish
the well-posedness of each optimization problem, characterize the corresponding
minimizers, and solve them by means of proximal splitting algorithms
originating from the realm of non-smooth convex optimization theory.
Experimental results are conducted to demonstrate the potential applicability
of the proposed algorithms to astronomical imaging datasets
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