Optimal Smoothing of Noisy Data Using Spline Functions

Florencio Utreras D.

doi:10.1137/0902028

Optimal Smoothing of Noisy Data Using Spline Functions

SIAM Journal on Scientific and Statistical Computing ◽

10.1137/0902028 ◽

1981 ◽

Vol 2 (3) ◽

pp. 349-362 ◽

Cited By ~ 33

Author(s):

Florencio Utreras D.

Keyword(s):

Noisy Data ◽

Spline Functions ◽

Optimal Smoothing

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Optimal knot selection for least-squares fitting of noisy data with spline functions

2008 IEEE Instrumentation and Measurement Technology Conference ◽

10.1109/imtc.2008.4546998 ◽

2008 ◽

Cited By ~ 1

Author(s):

Jerome Blair

Keyword(s):

Least Squares ◽

Noisy Data ◽

Spline Functions ◽

Least Squares Fitting ◽

Selection For

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Smoothing Noisy Data Using Dynamic Programming and Generalized Cross-Validation

Journal of Biomechanical Engineering ◽

10.1115/1.3108403 ◽

1988 ◽

Vol 110 (1) ◽

pp. 37-41 ◽

Cited By ~ 30

Author(s):

C. R. Dohrmann ◽

H. R. Busby ◽

D. M. Trujillo

Keyword(s):

Dynamic Programming ◽

Cross Validation ◽

Present Model ◽

Noisy Data ◽

Smoothing Parameter ◽

Spline Functions ◽

General Context ◽

Simple Extension ◽

Generalized Cross Validation ◽

Selection Of

Smoothing and differentiation of noisy data using spline functions requires the selection of an unknown smoothing parameter. The method of generalized cross-validation provides an excellent estimate of the smoothing parameter from the data itself even when the amount of noise associated with the data is unknown. In the present model only a single smoothing parameter must be obtained, but in a more general context the number may be larger. In an earlier work, smoothing of the data was accomplished by solving a minimization problem using the technique of dynamic programming. This paper shows how the computations required by generalized cross-validation can be performed as a simple extension of the dynamic programming formulas. The results of numerical experiments are also included.

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Splines

Selected Topics in Approximation and Computation ◽

10.1093/oso/9780195080599.003.0005 ◽

1995 ◽

Author(s):

Marek A. Kowalski ◽

Krzystof A. Sikorski ◽

Frank Stenger

Keyword(s):

Computer Graphics ◽

Numerical Solutions ◽

Noisy Data ◽

Spline Functions ◽

Complexity Bounds ◽

B Splines ◽

Approximation Errors ◽

Linear Problems ◽

High Degree ◽

Polynomial Methods

Spline functions are important approximation tools in numerous applications for which high degree polynomial methods perform poorly, such as in computer graphics and geometric modelling, as well as for various engineering problems—especially those involving graphing of numerical solutions and noisy data. Algorithms based on spline functions enjoy minimal approximation errors in wide classes of problems and minimal complexity bounds. In this Chapter we provide a brief introduction to basic classes of polynomial splines, B-Splines, and abstract splines. Further study of spline algorithms as applied to linear problems is outlined in Chapter 7. In this section we define polynomial spline functions, exhibit their interpolatory properties, and construct algorithms to compute them. It turns out that these splines provide interpolating curves that do not exhibit the large oscillations associated with high degree interpolatory polynomials. This is why they find applications in univariate curve matching in computer graphics.

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