Automatic smoothing by optimal splines

Abstract

We propose a method that is capable to filter out noise as well as suppress outliers of sampled real functions under fairly general conditions. From an a priori selection of the number of knots that define the adjusting spline, but not their location in that curve, the method automatically determines the adjusting cubic spline in a least-squares optimal sense. The method is fast and easily allows for selection of various possible number of knots, adding a desirable flexibility to the procedure. As an illustration, we apply the method to some typical situations found in geophysical problems.Keywords: Smoothing, cubic splines RESUMO Propomos um método capaz de filtrar ruído bem como suprimir outliers de uma função real amostrada, impondo praticamente nenhuma condição. A partir de uma seleção a priori da quantidade de nós que definirão a spline, porém não suas localizações, o método automaticamente determina a spline cúbica que melhor ajusta os dados, no sentido de quadrados mínimos. Dado que o método é rápido, torna-se viável a realização de vários ajustes com quantidades distintas de nós, conferindo assim a flexibilidade desejada ao processo. Como exemplo, aplicamos o método a alguns problemas em Geofísica.Palavras-chave: suavização, spline cúbica

Application of the Automatic Optimal Spline Smoothing Method to Optimizing Edges of Moroccan Bouguer Gravity Anomaly Map

“…On the other extreme, for large values of N , the spline will tend to fit even the outliers. Since the method is fast, it is reasonable to estimate cubic spline for several choices of N [18] [19]. This flexibility can be very useful to the user or interpreter, in the sense that a number of inexpensive trials can be implemented before a final decision on which level of smoothness is the best choice for the problem.…”

Strain Field Interpolation Over the Sciara Del Fuoco (Stromboli Volcano) From Geodetic Measurements Acquired by the Automatic Theodoros System

“…Although both spikes and offsets removal makes ground deformations more readable, further processing is needed to reduce noise source affecting data, in particular the thermoelastic effects on ground deformation due to the temperature. To this purpose we have smoothed noisy data with spline functions following the suggestion of the literature (Biloti et al, 2008), (Ge et al, 2003). A spline function s(t) is a function defined piecewise by polynomials.…”

A frequency criterion for optimal node selection in smoothing with cubic splines

“…The method to determine the approximation of a given function by optimal cubic splines detects the best positions of the given number of nodes. The objective function is the deviation of the smoothed function from the original function to be approximated (Biloti et al . 2003).…”

“…Recently, an extension of optimal spline approximation (Reinsch 1967) has been proposed (Biloti 2001; Biloti, Santos and Tygel 2002, 2003; Goldenthal and Bercovier 2004), which allows repositioning of the nodes when minimizing the misfit between the original and approximate functions in a least‐squares sense. This technique differs from standard smoothing spline interpolation (de Boor 1978) in the fact that the node positions are no longer fixed but also allowed to vary.…”