131 research outputs found
A Collection of Optimal Control Problems
In this work, a collection of elliptic and parabolic control problems with control and state constraints is described, focusing on the discretization techniques which yield to Nonlinear Programming (NLP) problems having large, sparse and structured Hessian and Jacobian matrices. The collection includes 25 elliptic and parabolic control problem, which are described in detail, reporting the sparsity pattern of the Hessian and Jacobian matrices. The figures depicting the discrete solutions of the elliptic problems are also reported. The AMPL models of the elliptic control problems can be downloaded from the prof. Mittelmann's web page http://plato.asu.edu/ftp/ampl_files/ellip_ampl/ while the ones related to the parabolic ones are downloadable from http://dm.unife.it/~bonettini/ip_pcg/controllo.ht
Accelerated gradient methods for the X-ray imaging of solar flares
In this paper we present new optimization strategies for the reconstruction
of X-ray images of solar flares by means of the data collected by the Reuven
Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The imaging concept of
the satellite is based of rotating modulation collimator instruments, which
allow the use of both Fourier imaging approaches and reconstruction techniques
based on the straightforward inversion of the modulated count profiles.
Although in the last decade a greater attention has been devoted to the former
strategies due to their very limited computational cost, here we consider the
latter model and investigate the effectiveness of different accelerated
gradient methods for the solution of the corresponding constrained minimization
problem. Moreover, regularization is introduced through either an early
stopping of the iterative procedure, or a Tikhonov term added to the
discrepancy function, by means of a discrepancy principle accounting for the
Poisson nature of the noise affecting the data
On an iteratively reweighted linesearch based algorithm for nonconvex composite optimization
In this paper we propose a new algorithm for solving a class of nonsmooth nonconvex problems, which is obtained by combining the iteratively reweighted scheme with a finite number of forward–backward iterations based on a linesearch procedure. The new method overcomes some limitations of linesearch forward–backward methods, since it can be applied also to minimize functions containing terms that are both nonsmooth and nonconvex. Moreover, the combined scheme can take advantage of acceleration techniques consisting in suitable selection rules for the algorithm parameters. We develop the convergence analysis of the new method within the framework of the Kurdyka– Lojasiewicz property. Finally, we present the results of a numerical experience on microscopy image super resolution, showing that the performances of our method are comparable or superior to those of other algorithms designed for this specific application
Shearlet-based regularized reconstruction in region-of-interest computed tomography
Region of interest (ROI) tomography has gained increasing attention in recent years due to its potential to reducing radiation exposure and shortening the scanning time. However, tomographic reconstruction from ROI-focused illumination involves truncated projection data and typically results in higher numerical instability even when the reconstruction problem has unique solution. To address this problem, both ad hoc analytic formulas and iterative numerical schemes have been proposed in the literature. In this paper, we introduce a novel approach for ROI tomographic reconstruction, formulated as a convex optimization problem with a regularized term based on shearlets. Our numerical implementation consists of an iterative scheme based on the scaled gradient projection method and it is tested in the context of fan-beam CT. Our results show that our approach is essentially insensitive to the location of the ROI and remains very stable also when the ROI size is rather small.Peer reviewe
A convergent blind deconvolution method for post-adaptive-optics astronomical imaging
In this paper we propose a blind deconvolution method which applies to data
perturbed by Poisson noise. The objective function is a generalized
Kullback-Leibler divergence, depending on both the unknown object and unknown
point spread function (PSF), without the addition of regularization terms;
constrained minimization, with suitable convex constraints on both unknowns, is
considered. The problem is nonconvex and we propose to solve it by means of an
inexact alternating minimization method, whose global convergence to stationary
points of the objective function has been recently proved in a general setting.
The method is iterative and each iteration, also called outer iteration,
consists of alternating an update of the object and the PSF by means of fixed
numbers of iterations, also called inner iterations, of the scaled gradient
projection (SGP) method. The use of SGP has two advantages: first, it allows to
prove global convergence of the blind method; secondly, it allows the
introduction of different constraints on the object and the PSF. The specific
constraint on the PSF, besides non-negativity and normalization, is an upper
bound derived from the so-called Strehl ratio, which is the ratio between the
peak value of an aberrated versus a perfect wavefront. Therefore a typical
application is the imaging of modern telescopes equipped with adaptive optics
systems for partial correction of the aberrations due to atmospheric
turbulence. In the paper we describe the algorithm and we recall the results
leading to its convergence. Moreover we illustrate its effectiveness by means
of numerical experiments whose results indicate that the method, pushed to
convergence, is very promising in the reconstruction of non-dense stellar
clusters. The case of more complex astronomical targets is also considered, but
in this case regularization by early stopping of the outer iterations is
required
Improving the angular resolution of coded aperture instruments using a modified Lucy-Richardson algorithm for deconvolution
A problem with coded-mask telescopes is the achievable angular resolution. For example, with the standard cross-correlation (CC) analysis, the INTEGRAL IBIS/ISGRI angular resolution is about 13'. We are currently investigating an iterative Lucy-Richardson (LR) algorithm. The LR algorithm can be used effectively when the PSF is known, but little or no information is available for the noise. This algorithm maximizes the probability of the restored image, under the assumption that the noise is Poisson distributed, which is appropriate for photon noise in the data, and converges to the maximum likelihood solution. We have modified the classical LR algorithm, adding non-negative constraints. It doesn't take into account of the features leading to a difference in PSF depending on position in the field of view (dead pixels, gaps between modules etc), which are easily corrected for in the classical CC analysis, so we must correct for these either after the restoration of the image or by modifing the data before the sky reconstruction. We present some results using real IBIS data indicating the power of the proposed reconstruction algorithm
Efficient Bayesian-based Multi-View Deconvolution
Light sheet fluorescence microscopy is able to image large specimen with high
resolution by imaging the sam- ples from multiple angles. Multi-view
deconvolution can significantly improve the resolution and contrast of the
images, but its application has been limited due to the large size of the
datasets. Here we present a Bayesian- based derivation of multi-view
deconvolution that drastically improves the convergence time and provide a fast
implementation utilizing graphics hardware.Comment: 48 pages, 20 figures, 1 table, under review at Nature Method
Preconditioned ADMM with nonlinear operator constraint
We are presenting a modification of the well-known Alternating Direction
Method of Multipliers (ADMM) algorithm with additional preconditioning that
aims at solving convex optimisation problems with nonlinear operator
constraints. Connections to the recently developed Nonlinear Primal-Dual Hybrid
Gradient Method (NL-PDHGM) are presented, and the algorithm is demonstrated to
handle the nonlinear inverse problem of parallel Magnetic Resonance Imaging
(MRI)
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