Wavelet basis reconstruction of nonuniformly sampled data

Abstract

A well-documented problem in the analysis of real-world measurements is that the data may suffer from several problems, including data dropouts, an irregularly spaced sampling grid, and time-delayed sampling. These data irregularities render many traditional signal processing techniques unusable, and thus the data must be interpolated onto an even grid before scientific analysis techniques can be applied. We propose a method to perform a reconstruction of nonuniformly sampled signals using a wavelet basis fit in a multiresolutional setting. The advantage of using a wavelet basis is that we are able to not only reconstruct the signal using global information, but we are also able to take advantage of locally dense areas of sampling to reconstruct at higher resolutions.