ENHANCED MULTIRESOLUTION ANALYSIS FOR MULTIDIMENSIONAL DATA UTILIZING LINE FILTERING TECHNIQUES br

In this article we introduce line Smoothness-Increasing Accuracy-Conserving Multi -Resolution Analysis. This is a procedure for exploiting convolution kernel post-processors for ob-taining more accurate multidimensional multiresolution analysis in terms of error reduction. This filtering-projection tool allows for the transition of data between different resolutions while simultane-ously decreasing errors in the fine grid approximation. It specifically allows for defining detail multi -wavelet coefficients when translating coarse data onto finer meshes. These coefficients are usually not defined in such cases. We show how to analytically evaluate the resulting convolutions and express the filtered approximation in a new basis. This is done by combining the filtering procedure with projection operators that allow for computational implementation of this scale transition procedure. Further, this procedure can be applied to piecewise constant approximations to functions, as it pro-vides error reduction. We demonstrate the effectiveness of this technique in two and three dimensions.

Automated summary

In this article, we introduce a procedure called line Smoothness-Increasing Accuracy-Conserving Multi-Resolution Analysis, which utilizes convolution kernel post-processors to obtain more accurate multidimensional multiresolution analysis by reducing errors. This procedure allows for data transition between different resolutions while simultaneously decreasing errors in fine grid approximation. It specifically defines detail multi-wavelet coefficients when translating coarse data onto finer meshes, which are usually not defined in such cases. We show how to evaluate the resulting convolutions analytically and express the filtered approximation in a new basis. This procedure can be applied to piecewise constant approximations to functions and provides error reduction. We demonstrate the effectiveness of this technique in two and three dimensions.