Multiscale analysis by means of discrete mollification for ecg noise reduction

Abstract

Multiscale analysis and computation is a rapidly evolving area of research that have had a fundamental impact on computational science and applied mathematics and have influenced the way we view the relation between mathematics and science. Even though multiscale problems have been longly studied in mathematics, such techniques suffer of the ill-posedness nature of the problem. In the solution of several ill-posed problems, discrete mollification has been used for regularization. In this paper, we propose a new technique (procedure) for multiscale analysis by using discrete mollification. The multiscale scheme is based on numerical linear algebra results combined with the mollification method applied to the Mallat algorithm. The new technique has a simple theory, an efficient implementation and compares fairly well with classical wavelet transform procedures. An application on electrocardiographic signals contaminated with typical non-white noise is considered.