Two dimensional smoothing via an optimised Whittaker smoother

Abstract

In many applications where moderate to large datasets are used, plotting relationships between pairs of variables can be problematic. A large number of observations will produce a scatter-plot which is difficult to investigate due to a high concentration of points on a simple graph. In this article we review the Whittaker smoother for enhancing scatter-plots and smoothing data in two dimensions. To optimise the behaviour of the smoother an algorithm is introduced, which is easy to programme and computationally efficient. The methods are illustrated using a simple dataset and simulations in two dimensions. Additionally, a noisy mammography is analysed. When smoothing scatterplots the Whittaker smoother is a valuable tool that produces enhanced images that are not distorted by the large number of points. The methods is also useful for sharpening patterns or removing noise in distorted images. The Whittaker smoother can be a valuable tool in producing better visualisations of big data or filter distorted images. The suggested optimisation method is easy to programme and can be applied with low computational cost.