An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations sufficiently well. Although the regularizer and constraint are usually convex, several particular features of these problems (huge dimensionality, non-smoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications. The proposed algorithm, which belongs to the family of augmented Lagrangian methods, can be used to deal with a variety of imaging IPLIP, including deconvolution and reconstruction from compressive observations (such as MRI), using either total-variation or wavelet-based (or, more generally, frame-based) regularization. The proposed algorithm is an instance of the so-called "alternating direction method of multipliers", for which convergence sufficient conditions are known; we show that these conditions are satisfied by the proposed algorithm. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is a strong contender for the state-of-the-art.Comment: 13 pages, 8 figure, 8 tables. Submitted to the IEEE Transactions on Image Processin

Fast Image Recovery Using Variable Splitting and Constrained Optimization

We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a non-smooth regularizer. This formulation allows both wavelet-based (with orthogonal or frame-based representations) regularization or total-variation regularization. Our approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is then addressed with an augmented Lagrangian method. The proposed algorithm is an instance of the so-called "alternating direction method of multipliers", for which convergence has been proved. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is faster than the current state of the art methods.Comment: Submitted; 11 pages, 7 figures, 6 table

Análise dos principais determinantes do empreendedorismo em Portugal

Without question, entrepreneurship is present in all spheres of our lives, especially in economic and social areas. This field is significant in the development of societies and is also considered a useful tool in promoting innovation and job creation in many countries. For this reason, it needs to be promoted as a central component of economic growth. As a result, the creation of new businesses or projects and the promotion of self-employment have been stimulated by public and private organisations. The goal of this research is to determine what triggers individuals to be actively involved in entrepreneurial activity in the initial phases, based on a survey by Global Entrepreneurship Monitor conducted in Portugal, in 2012. The results of this analysis revealed that early-stage entrepreneurial activity is associated with younger (25–34 years old) males, who have a medium to higher level of household income, as well as diplomas. They are self-employed, and they have loose ties to other entrepreneurs. They perceive themselves as possessing entrepreneurial skills and have a low level of perceived risk and a positive personal attitude towards individual innovation.info:eu-repo/semantics/publishedVersio

Superinflation, quintessence, and the avoidance of the initial singularity

We consider the dynamics of a spatially flat universe dominated by a self-interacting nonminimally coupled scalar field. The structure of the phase space and complete phase portraits for the conformal coupling case are given. It is shown that the non-minimal coupling modifies drastically the dynamics of the universe. New cosmological behaviors are identified, including superinflation ($\dot{H}>0$), avoidance of big bang singularities through classical birth of the universe from empty Minkowski space, and spontaneous entry into and exit from inflation. The relevance of this model to the description of quintessence is discussed.Comment: RevTex, 10 pages, 4 figures, To appear in the proceedings of the 5th Peyresq meetin

Acyclic orientations with path constraints

Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions of the vertex coloring and frequency assignment problems. In this paper we introduce a linear programming formulation of acyclic orientations with path constraints, and discuss its use in the solution of the vertex coloring problem and some versions of the frequency assignment problem. A study of the polytope associated with the formulation is presented, including proofs of which constraints of the formulation are facet-defining and the introduction of new classes of valid inequalities

Online-learning at ISCTE-IUL: towards a sustainable education paradigm

Online-learning platforms have long been praised for their great benefits, such as the way they contribute to long-distance students being able to overcome geographical barriers to their education, and the way they allow students to self-manage, by autonomously deciding when they enroll and complete courses. This empowers people from all over the world to engage in lifelong-learning that may have an important impact in their daily lives, especially in developing countries. Besides these benefits, there’s also an important dimension that is often overlooked: the contribution that the use of online-learning platforms has in providing a sustainable environment by reducing environmentally-damaging effects and the use of scarce resources. In this paper, we present the economical and environmental impact that the use of an online-learning platform has had in a public University in Lisbon, Portugal. We first present the online-learning platform that was developed in-house and follow up by describing the positive impact that this education paradigm has had in the lives of students, in reducing costs at the University, and in contributing to a more sustainable future.info:eu-repo/semantics/acceptedVersio