One- and two-dimensional least-squares smoothing and edge-sharpening method for image processing

A rapid method is developed for two-dimensional smoothing and edge-sharpening by the least-squares fitting of a function to a limited area of the data. This convolution or matrix weighting is applied at each point of the data set to yield a smoothed or a sharpened image. Weighting matrices for 3 x 3, 5 x 5, and 7 x 7 point fitting areas are provided for polynomial function fits of all degrees up to the highest degree determinable. For the 7 x 7 point fitting area weights for fitting functions of up to the quartic in both dimensions are supplied. Application of the 5 x 5 point quadratic fit smoothing to a nuclear medicine image is shown as an example