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In recent years, several efforts were made in order to introduce boundary conditions for deblurring problems that allow to get accurate reconstructions. This resulted in the birth of Reflective, Anti-Reflective and Mean boundary conditions, which are all based on the idea of guaranteeing the continuity of the signal/image outside the boundary. Here we propose new boundary conditions that are obtained by suitably combining Taylor series and finite difference approximations. Moreover, we show that also Anti-Reflective and Mean boundary conditions can be attributed to the same framework. Numerical results show that, in case of low levels of noise and blurs able to perform a suitable smoothing effect on the original image (e.g. Gaussian blur), the proposed boundary conditions lead to a significant improvement of the restoration accuracy with respect to those available in the literature. [ABSTRACT FROM AUTHOR]

Regularizing preconditioners for accelerating the convergence of iterative regularization methods without spoiling the quality of the approximated solution have been extensively investigated in the last twenty years. Several strategies have been proposed for defining proper preconditioners. Usually, in methods for image restoration, the structure of the preconditioner is chosen Block Circulant with Circulant Blocks (BCCB) because it can be efficiently exploited by Fast Fourier Transform (FFT). Nevertheless, for ill-conditioned problems, it is well-known that BCCB preconditioners cannot provide a strong clustering of the eigenvalues. Moreover, in order to get an effective preconditioner, it is crucial to preserve the structure of the coefficient matrix. The structure of such a matrix, in case of image deblurring problem, depends on the boundary conditions imposed on the imaging model. Therefore, we propose a technique to construct a preconditioner which has the same structure of the blurring matrix related to the restoration problem at hand. The construction of our preconditioner requires two FFTs like the BCCB preconditioner. The presented preconditioning strategy represents a generalization and an improvement with respect to both circulant and structured preconditioning available in the literature. The technique is further extended to provide a non-stationary preconditioning in the same spirit of a recent proposal for BCCB matrices. Some numerical results show the importance of preserving the matrix structure from the point of view of both restoration quality and robustness of the regularization parameter. [ABSTRACT FROM AUTHOR]

Image restoration problem is an important topic which appears in many different scientific areas. Several solving techniques are available, but generally in real applications, from which large-scale linear systems arise, the choice falls on iterative algorithms. In particular statistical methods (Lucy-Richardson method, image space reconstruction algorithm) have been extensively studied in the literature. Since they have low convergence rates, it is necessary to employ acceleration strategies. At this time, the most popular is the one introduced in 1997 by Biggs and Andrews, called automatic acceleration by the authors. In the present paper we describe $$\nu $$ acceleration, that is the translation of the idea behind $$\nu $$ -method, conceived for speeding up Landweber method, in the context of statistical methods. Computational results, which compare accelerated and classical methods, show the effectiveness of this strategy, which is able to get better performance than automatic acceleration. [ABSTRACT FROM AUTHOR]

An acceleration technique for multiplicative iterative methods, such as Lucy–Richardson and Image Space Reconstruction Algorithm, is presented. The technique is inspired by the Landweber method in Banach spaces and is based on the application of duality maps, which allow to compute the iterations in the dual space. We show the link between the proposed acceleration and the previously known Meinel acceleration, which consists in the introduction of an exponent in the basic iterative formulas. We prove that the new acceleration technique is more stable than the Meinel acceleration. This implies that, in the restoration process, the former is able to get better accuracy and higher speeding-up than the latter. In addition to the main focus of the paper, we propose a generalization of the Landweber method in Banach space, in order to overcome some drawbacks of this recent strategy when compared with classical (Hilbertian) Landweber method. Numerical results show the behavior and the features of the several techniques considered, highlighting the goodness of our proposals. [ABSTRACT FROM AUTHOR]

We analyse the practical efficiency of multi-iterative techniques for the numerical solution of graph-structured large linear systems. In particular we evaluate the effectiveness of several combinations of coarser-grid operators which preserve the graph structure of the projected matrix at the inner levels and smoothers. We also discuss and evaluate some possible strategies (inverse projection and dense projection) to connect coarser-grid operators and graph-based preconditioners. Our results show that an appropriate choice of adaptive projectors and tree-based preconditioned conjugate gradient methods result in highly effective and robust approaches, that are capable to efficiently solve large-scale, difficult systems, for which the known iterative solvers alone can be rather slow. [ABSTRACT FROM AUTHOR]

Traffic flow prediction is a fundamental functionality of intelligent transportation systems. After presenting the state of the art, we focus on nearest neighbor regression methods, which are data-driven algorithms that are effective yet simple to implement. We try to strengthen their efficacy in two ways that are little explored in literature, i.e., by adopting a multivariate approach and by adding awareness of the time of the day. The combination of these two refinements, which represents a novelty, leads to the definition of a new class of methods that we call time-aware multivariate nearest neighbor regression (TaM-NNR) algorithms. To assess this class, we have used publicly available traffic data from a California highway. Computational results show the effectiveness of such algorithms in comparison with state-of-the-art parametric and non-parametric methods. In particular, they consistently perform better than their corresponding standard univariate versions. These facts highlight the importance of context elements in traffic prediction. The ideas presented here may be further investigated considering more context elements (e.g., weather conditions), more complex road topologies (e.g., urban networks), and different types of prediction methods. [ABSTRACT FROM PUBLISHER]

It is well known that iterative algorithms for image deblurring that involve the normal equations show usually a slow convergence. A variant of the normal equations which replaces the conjugate transpose AH of the system matrix A with a new matrix is proposed. This approach, which is linked with regularization preconditioning theory and reblurring processes, can be applied to a wide set of iterative methods; here we examine Landweber, Steepest descent, Richardson-Lucy and Image Space Reconstruction Algorithm. Several computational tests show that this strategy leads to a significant improvement of the convergence speed of the methods. Moreover it can be naturally combined with other widely used acceleration techniques. [ABSTRACT FROM AUTHOR]