1,720,997 research outputs found
Optimization Methods for Image Regularization from Poisson Data
Full text linkThis work regards optimization techniques for image restoration problems in presence
of Poisson noise. In several imaging applications (e.g. Astronomy, Microscopy, Medical
Imaging) such noise is predominant; hence regularization techniques are needed in order
to obtain satisfying restored images. In a variational framework, the image restoration
problem consists in finding a minimum of a functional, which is the sum of two terms,:
the fit–to–data and the regularization one. The trade–off between these two terms is
measured by a regularization parameter. The estimation of such a parameter is very
difficult due to the presence of Poisson noise. In this thesis we investigate three models
regarding this parameter: a Discrepancy Model, Constrained Model and the Bregman
procedure. The former two provide an estimation for the regularization parameter,
but in some cases, such as low counts images, they do not allow to obtain satisfactory
results. On the other hand, in presence of such images the Bregman procedure provides
reliable results and, moreover, it allows to use an overestimation of the regularization
parameter, giving satisfying restored images; furthermore, this procedure permits to
gain a contrast enhancement on the final result.
In the first part of the work, the basics on image restoration problems are recalled, and
a survey on the state–of–the–art methods is given, with an original contribution regarding
scaling techniques in ε–subgradient methods. Then, the Discrepancy and the
Constrained Models are analyzed from both theoretical and practical point of view,
developing suitable numerical techniques for their solution; furthermore, an inexact
version of the Bregman procedure is introduced: such a version allows to have a minor
computational cost and maintains the same theoretical features of the exact version.
Finally, in the last part, a wide experimentation shows the computational efficiency of
the inexact Bregman procedure; furthermore, the three models are compared, showing
that in high counts images they provide similar results, while in case of low counts images
the Bregman procedure provides reliable restored images. This last consideration
is evident not only on test problems, but also in problems coming from Astronomy
imaging, particularly in case of High Dynamic Range images, as shown in the final part
of the experimental section
Constrained Plug-and-Play Priors for Image Restoration
Full text linkThe Plug-and-Play framework has demonstrated that a denoiser can implicitly serve as the image prior for model-based methods for solving various inverse problems such as image restoration tasks. This characteristic enables the integration of the flexibility of model-based methods with the effectiveness of learning-based denoisers. However, the regularization strength induced by denoisers in the traditional Plug-and-Play framework lacks a physical interpretation, necessitating demanding parameter tuning. This paper addresses this issue by introducing the Constrained Plug-and-Play (CPnP) method, which reformulates the traditional PnP as a constrained optimization problem. In this formulation, the regularization parameter directly corresponds to the amount of noise in the measurements. The solution to the constrained problem is obtained through the design of an efficient method based on the Alternating Direction Method of Multipliers (ADMM). Our experiments demonstrate that CPnP outperforms competing methods in terms of stability and robustness while also achieving competitive performance for image quality
Nonlinear microscale interactions in the kinetic theory of active particles
Full text linkThe aim of this note is to examine the sources of nonlinearity arising in the kinetic theory of active particles. We show how nonlinearities enter the different terms of the theory, giving rise to possible developments toward the modeling of different types of complex systems, mainly living and social ones, where proliferative-destructive processes must be included. Finally, some research perspectives are discussed
Image regularization for Poisson data
Full text linkRecently, Poisson noise has become of great interest in many imaging applications. When regularization strategies are used in the so-called Bayesian approach, a relevant, issue is to find rules for selecting 1 proper value of the regularization parameter. In this work we compare three different approaches which deal with this topic. The first model anus to find the root of a discrepancy equation, while the second one estimates such parameter by adopting a constrained approach. These two models do not always provide reliable results in presence of low counts images. The third approach presented is the inexact Bregman procedure, which allows to use an overestimation of the regularization parameter and moreover enables to obtain very promising results in case of low counts images and High Dynamic Range astronomical images
Constrained Regularization by Denoising With Automatic Parameter Selection
No full textRegularization by Denoising (RED) is a well-known method for solving image restoration problems by using learned image denoisers as priors. Since the regularization parameter in the traditional RED does not have any physical interpretation, it does not provide an approach for automatic parameter selection. This letter addresses this issue by introducing the Constrained Regularization by Denoising (CRED) method that reformulates RED as a constrained optimization problem where the regularization parameter corresponds directly to the amount of noise in the measurements. The solution to the constrained problem is solved by designing an efficient method based on alternating direction method of multipliers (ADMM). Our experiments show that CRED outperforms the competing methods in terms of stability and robustness, while also achieving competitive performances in terms of image quality
Inexact Bregman iteration with an application to Poisson data reconstruction
No full textThis 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 Kullback–Leibler divergence combined with
a regularization term. The results of several numerical experiments enable to evaluat
Inexact Bregman iteration for deconvolution of superimposed extended and point sources
No full textIn this paper we consider the deconvolution of high contrast images consisting of very bright stars (point component) and smooth structures underlying the stars (diffuse component). A typical case is a weak diffuse jet line emission superimposed to a strong stellar continuum. In order to reconstruct the diffuse component, the original object can be regarded as the sum of these two components. When the position of the point sources is known, a regularization term can be introduced for the second component. An approximation of the original object can be obtained by solving a reduced variational problem whose unknowns are the intensities of the stars and the diffuse component. We analyze this problem when the detected image is corrupted by Poisson noise and Tikhonov-like regularization is used, giving conditions for the existence and the uniqueness of the solution. Furthermore, since only an overestimation of the regularization parameter is available, we propose to solve the variational problem by inexact Bregman iteration combined with a Scaled Gradient Projection method (SGP). Numerical simulations show that the images obtained with this approach enable us to reconstruct the original intensity distribution around the point source with satisfactory accuracy
Modeling opinion formation in the kinetic theory of active particles I : Spontaneous trend
No full textThe kinetic theory of active particles is used to model the formation and evolution of opinions in a structured population. The spatial structure is modeled by a network whose nodes mimic the geographic distribution of individuals, while the functional subsystems present in each node group together elements sharing a common orientation. In this paper we introduce a model, based on nonlinear and nonlinearly additive interactions among individuals, subsystems and nodes, related to the spontaneous evolution of opinion concerning given specific issues. Numerical solutions in a model situation not related with real data show how the mutual interactions are able to drive the subsystems opinion toward the emergence of collective structures characterizing this kind of complex systems
Advanced Techniques in Optimization for Machine Learning and Imaging
No full textIn recent years, non-linear optimization has had a crucial role in the development of modern techniques at the interface of machine learning and imaging. The present book is a collection of recent contributions in the field of optimization, either revisiting consolidated ideas to provide formal theoretical guarantees or providing comparative numerical studies for challenging inverse problems in imaging. The work of these papers originated in the INdAM Workshop “Advanced Techniques in Optimization for Machine learning and Imaging” held in Roma, Italy, on June 20-24, 2022.
The covered topics include non-smooth optimisation techniques for model-driven variational regularization, fixed-point continuation algorithms and their theoretical analysis for selection strategies of the regularization parameter for linear inverse problems in imaging, different perspectives on Support Vector Machines trained via Majorization-Minimization methods, generalization of Bayesian statistical frameworks to imaging problems, and creation of benchmark datasets for testing new methods and algorithms
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