Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Aggregates of the Warmian-Masurian region as a solution for carrying out the road construction works

W artykule zwrócono uwagę na rosnący deficyt kruszywa łamanego ze skał litych. Deficyt oraz koszty transportu tego typu kruszyw z południa Polski w znacznym stopniu utrudniają realizację znaczących inwestycji regionu Warmii i Mazur, zwłaszcza w drogownictwie. W oparciu o wyniki badań przeprowadzonych przez autorów oraz rezultaty badań publikowanych autorzy wykazują, że kruszywa naturalne z kopalń woj. warmińsko-mazurskiego spełniają wymagania stawiane kruszywom drogowym i popierają ich zastosowanie w elementach konstrukcji nawierzchni. Zwracają także uwagę na możliwość zmniejszenie nakładów finansowych przy realizacji takich inwestycji w regionie Warmii i Mazur.The article notes the fact that an expanding deficit appears, when it comes to the crushed-stone aggregate created with the use of rocks. Deficit and costs of transport pertaining to such aggregate, with shipments being sent from the southern part of Poland, make it significantly more difficult to implement relevant investments in the Warmian-Masurian region, especially when it comes to the road infrastructure. On the basis of the results of the research carried out by the authors, and the results of the research which had been already published, the researchers make an attempt at proving that natural aggregate coming from the mines located in the Warmian-Masurian Voivodeship meet the requirements defined for the road-building aggregate. The authors endorse application of the said aggregate in the works related to creation of new road surfaces. The Article also stresses the possible reduction of the financial expenditure, when such investments are realized in the Warmian-Masurian region

The role of microfillers in shaping the sulphur concrete performance

The article presents the research results of sulphur concrete - the material that is created at high temperature as a mixture of a sulphur binder with aggregate and microfillers. While it has very interesting properties, it is not as appreciated as it should be. The aim of this paper is also to encourage a deeper insight into the presented material, and the use of its hidden potential. Sulphur concrete is not new a product of modern technology - it has been known for decades, but new applications are still being found. The paper focuses mostly on the impact of the microfillers used on some properties of the concrete. In the research, the microfillers used were: fly ash, microsilica and zeolite. The article presents the microfillers’ influence on the growing kinetics of compressive and flexural strength and the effects of abrasion on the sulphur concrete. The lab tests were carried out after 3, 7 and 28 days. The most noticeable was the positive influence of the fly ash on concrete performance. The microfillers that influenced the material’s microstructure were also presented

Thermokinetic aspects of predicting the efficency of concrete admixtures

Domieszki odgrywają znaczną rolę we współczesnej technologii betonu. Efektywne ich wykorzystanie jest jednak bardzo często utrudnione ze względu na złożony mechanizm oddziaływania na podstawowe stadia, takie jak: adsorpcja, rozpuszczanie, reakcje chemiczne i inne. Badania tych procesów jednoznacznie wskazują, że niezależnie od mechanizmów oddziaływania domieszek, wszystkie one wpływają na zmiany kinetyki przebiegu tych procesów, a tym samym na intensywność i wielkość efektów cieplnych. W oparciu o przeprowadzone badania opracowano podstawowe założenia i kryteria termokinetycznej oceny efektywności domieszek.Admixtures are significant in modern concrete technology. However, their effective use is very often difficult due to the complex mechanism of their influence on the main stages, such as: adsorption, dissolution, chemical reactions and others. The study of these processes clearly indicates that regardless of the admixture mechanisms of interactions, they all influence the kinetic course of these processes and thereby the intensity and magnitude of the thermal effects. Based on the studies the basic assumptions and criteria for assessing the effectiveness of thermokinetic admixtures have been developed

Sulphur concrete’s technology and its application to the building industry

This article is a scientific – review piece of work which purpose is to popularize the common knowledge of sulphur concrete – the material that has become more and more popular not only in countries with established market economy. In the article there are presented key phases of scientific studies concerning technology of the sulphur concrete, concrete modified with sulphur and its application in building industry. There is also presented methodology of sample preparations, technology of production and its main technical properties

The environmental management system in a building company in the aspect of the requirements of the PN-EN ISO 14001:2015-09 standard

The article presents the environmental management system in a building company from the process perspective which meets the requirements of the international ISO 14001 standard. A new issue of this document from September 2015 introduced essentials changes in the attitude of building the system, its structure and in ways of documentation. The article is to precede an attempt of working out the criteria and parameters of the effectiveness of the assumed structure of processes, which will be a subject of next article. In the first part of the article, the justification for using the process approach in building the environmental management system was depicted – the modern concept which determines the effectiveness of action. The second part presents the theoretical model of the process structure of the environmental management system, which when adopted to the needs of a given building company may become a basis for the preparation of an effective system in practice