Image Scaling by de la Vallée-Poussin Filtered Interpolation

We present a new image scaling method both for downscaling and upscaling, running with any scale factor or desired size. The resized image is achieved by sampling a bivariate polynomial which globally interpolates the data at the new scale. The method’s particularities lay in both the sampling model and the interpolation polynomial we use. Rather than classical uniform grids, we consider an unusual sampling system based on Chebyshev zeros of the first kind. Such optimal distribution of nodes permits to consider near-best interpolation polynomials defined by a filter of de la Vallée-Poussin type. The action ray of this filter provides an additional parameter that can be suitably regulated to improve the approximation. The method has been tested on a significant number of different image datasets. The results are evaluated in qualitative and quantitative terms and compared with other available competitive methods. The perceived quality of the resulting scaled images is such that important details are preserved, and the appearance of artifacts is low. Competitive quality measurement values, good visual quality, limited computational effort, and moderate memory demand make the method suitable for real-world applications

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

A unified approach to sparse signal processing

A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i

Wavelet and Multiscale Methods

Various scientific models demand finer and finer resolutions of relevant features. Paradoxically, increasing computational power serves to even heighten this demand. Namely, the wealth of available data itself becomes a major obstruction. Extracting essential information from complex structures and developing rigorous models to quantify the quality of information leads to tasks that are not tractable by standard numerical techniques. The last decade has seen the emergence of several new computational methodologies to address this situation. Their common features are the nonlinearity of the solution methods as well as the ability of separating solution characteristics living on different length scales. Perhaps the most prominent examples lie in multigrid methods and adaptive grid solvers for partial differential equations. These have substantially advanced the frontiers of computability for certain problem classes in numerical analysis. Other highly visible examples are: regression techniques in nonparametric statistical estimation, the design of universal estimators in the context of mathematical learning theory and machine learning; the investigation of greedy algorithms in complexity theory, compression techniques and encoding in signal and image processing; the solution of global operator equations through the compression of fully populated matrices arising from boundary integral equations with the aid of multipole expansions and hierarchical matrices; attacking problems in high spatial dimensions by sparse grid or hyperbolic wavelet concepts. This workshop proposed to deepen the understanding of the underlying mathematical concepts that drive this new evolution of computation and to promote the exchange of ideas emerging in various disciplines

Applied Mathematics and Computational Physics

As faster and more efficient numerical algorithms become available, the understanding of the physics and the mathematical foundation behind these new methods will play an increasingly important role. This Special Issue provides a platform for researchers from both academia and industry to present their novel computational methods that have engineering and physics applications

Full-field analysis of the dynamic behaviour of thermally stressed panels

This thesis details the research conducted over the course of three years under funding from the European Office of the United States Air Force (EOARD) and the Engineering and Physical Sciences Research Council (EPSRC) as a part of a long-standing effort to collect high-quality experimental data which can be used in the development and validation of predictive computational mechanics models. The focus of this study is on the acquisition of full-field displacement and temperature data when thermally and thermo-mechanically loading aerospace grade material panels as a means to study the effect of non-uniform temperature distributions on their dynamic behaviour at a component level (macroscale). The inclusion of this data in the development of a robust predictive model has also been investigated. To that end, a review of the existing literature is provided which highlights the current knowledge gaps in the modelling and experiments on the thermal and thermo-vibratory loading of panels, as well as the state-of-the-art in full-field data analysis. Initially, a finite element (FE) model was developed and compared to predictive and experimental data available in literature. This allowed for an investigation into the best practices to adopt in the development of a computational mechanics model with temperature-dependent material properties. It was found that a successful representation of experimental conditions strongly depends on the effective depiction of the thermal load and initial shape of the component. Then, a thin plate with free edges and constrained about its centre was heated using quartz lamps arranged in two different configurations and mechanically loaded using a shaker. Experimental modal analysis was used to acquire the resonant frequencies and mode shapes of the plate. Mode shapes were studied by exciting the plate to its first eleven resonant frequencies and acquiring displacement data using a Pulsed Laser Digital Image Correlation method (PL-DIC). Infra-red imaging was used to acquire temperature maps across the specimen. Experimentally-acquired temperature maps and measurements of the plate’s initial shape were included in a temperature-dependent FE model, developed according to the findings in the preliminary study, previously described. For the first time, experimental results showed the resonant response of the plate to strongly depend on the temperature distribution across the structure, correlating well with past predictive work in the literature. This was supported by the results from the finite element model, which were validated against experimental data and found to yield reliable predictions. The influence of temperature distribution in the deformation of panels was further investigated using a 1 mm plate with reinforced edges. The geometry was designed to emulate an aircraft’s skin with the reinforced edges performing the function of stringers and ribs. High temperatures were achieved using quartz lamps arranged in various configurations with controllable power output. PL-DIC was used to measure surface displacements and a commercially-available micro bolometer mapped the temperature distribution across the plate. Deflection results for the reinforced plate showed it to behave as a dynamic system that buckles out-of-plane when heated before relaxing to a steady state. It was demonstrated that the out-of-plane displacement experienced by the plate is strongly influenced by the in-plane spatial distribution of temperature