Diagnosing Homoscedasticity with the Power-weighted Smoothing Spline

Calculation of the smoothing spline with weighted roughness measure

The (cubic) smoothing spline, of Schoenberg [S64] and Reinsch [R67], [R71], has become the most commonly used spline, particularly after the introduction of generalized cross validation by Craven and Wahba [CW79] for an automatic choice of the smoothing parameter. It is the purpose of this note to derive the computational details, in terms of B-splines, for the construction of the weighted smoo...

Tomographic Reconstruction Using Information-Weighted Spline Smoothing

1 I n t r o d u c t i o n The CBP method for tomographic reconstruction is derived from a mathemat i cal idealization of tomographic imaging without consideration of statistical measurement errors. This idealization leads to the well-known ramp filter [1], whose frequency response has the unfortunate effect of amplifying high-frequency measurement noise. The conventional approach to reducing th...

Noniterative Tomographic Reconstruction Using Simultaneous Weighted Spline Smoothing and Deconvolution

In [1] we proposed a spatially-variant method for removing noise from tomographic projection data using weighted spline smoothing. The projection model in [1] was based on detectors with the same width as their spacing. A better approximation for the detector response of many tomographs is a rectangular function or Gaussian function whose width is twice the detector spacing. (Such systems are a...

Smoothing by Spline Functions

Smoothing an arc spline

Arc splines are G continuous curves made of circular arcs and straight-line segments. They have the advantages that the curvature of an arc spline is known and controlled at all but a finite number of points, and that the offset curve of an arc spline is another arc spline. Arc splines are used by computer-controlled machines as a natural curve along which to cut and are used by highway route p...