We introduce a new model for multiscale analysis of space-time echocardiographic sequences. The proposed nonlinear partial diierential equation, representing the multiscale analysis, lters the sequence with keeping of the space-time coherent structures. It combines the ideas of regularized Perona-Malik anisotropic diiusion and Galilean invariant movie multiscale analysis of Alvarez, Guichard, L...

Nature is observed at all scales; with multiscale modeling, scientists bring together several scales for a holistic analysis of a phenomenon. The models on these different scales may require significant but also heterogeneous computational resources, creating the need for distributed multiscale computing. A particularly demanding type of multiscale models, tightly coupled, brings with it a numb...

This chapter presents a statistical analysis of multiscale derivative measurements. Noisy images and multiscale derivative measurements made of noisy images are analyzed; the means and variances of the measured noisy derivatives are calculated in terms of the parameters of the probability distribution function of the initial noise function and the scale or sampling aperture. Normalized and unno...

MOTIVATIONS Physiological systems are ruled by mechanisms operating across multiple temporal scales. A recently proposed approach, multiscale entropy analysis, measures the complexity at different time scales and has been successfully applied to long term electrocardiographic recordings. The purpose of this work is to show the applicability of this methodology, rooted on statistical physics ide...

Abstract. This paper presents the multiscale analysis and numerical algorithms for the convectiondiffusion equations with rapidly oscillating periodic discontinuous coefficients. The multiscale asymptotic expansions are developed and an explicit rate of convergence is derived for the convex domains. An efficient multiscale hybrid FEM-FVM algorithm is constructed, and numerical experiments are r...

The analysis to detect arrhythmias and life-threatening conditions are highly essential in today world and this analysis can be accomplished by advanced non-linear processing methods for accurate analysis of the complex signals of heartbeat dynamics. In this perspective, recent developments in the field of multiscale information content have lead to the Microcanonical Multiscale Formalism (MMF)...

Bernard Jones told you about multiresolution analysis in his wavelet lectures. This is a pretty well formalized and self-contained area of wavelet analysis. Multiscale methods form a wider and less well defined area of tools and approaches; the term is used, e.g., in numerical analysis, but the main range of multiscale methods are based on application of wavelets. In this this lecture I shall e...

We describe a range of powerful multiscale analysis methods. We also focus on the pivotal issue of measurement noise in the physical sciences. From multiscale analysis and noise modeling, we develop a comprehensive methodology for data analysis of 2D images, 1D signals (or spectra), and point pattern data. Noise modeling is based on the following: (i) multiscale transforms, including wavelet tr...

We discuss a recently presented model for multiscale analysis of space-time sequences and its parallel implementation. Our nonlinear partial diierential equation, representing the multiscale analysis, lters the sequence while keeping of the space-time coherent structures. It combines the ideas of regularized Perona-Malik anisotropic diiusion and Galilean invariant movie multiscale analysis of A...