Reducing dimension of parametric space based on the approximation of components for interpolation of multidimensional signals

Abstract

In this paper, we address the problem of parametric space dimension reduction in the interpolation of multidimensional signals task. We develop adaptive parameterized interpolation algorithms for multidimensional signals. We perform a dimension reduction of the parameter space to reduce the complexity of optimizing such algorithms. The dependences of the samples inside the signal sections and between the signal sections are taken into account in various ways to reduce the dimension. We consider the dependencies between the signal sections through the approximation algorithm for the sections. We take into account the sample dependencies inside sections due to an adaptive parameterized interpolation algorithm. As a result, we solve the optimization problem of an adaptive interpolator in the parameter space of lower dimension for each signal section separately. To study the effectiveness of adaptive interpolators, we perform computational experiments using real-world multidimensional signals. Experimental results showed that the proposed interpolator improves the efficiency of the compression method up to 10% compared with the prototype algorithm.