Du e to the statistical nature of x-rays and the electromagnetic field, medical images produced by these energy sources are contaminated with random noise, which degrades the image quality. Because of this effect, considerable effort has been devoted to removing noise from medical images. A basic method for noise removal is image smoothing , which can be applied in both the frequency and the spatial domain. Sharp transitions, such as noise or edges, contribute heavily to the high-frequency content in the Fourier transform. Therefore, it follows that smoothing can be achieved with a low-pass filter. Alternatively, smoothing can be done in the spatial domain. Neighborhood averaging (e.g., the mean filter) is a straightforward technique for image smoothing. The difficulty with these two techniques is that both filters are applied indiscriminately and will blur the image. Another type of filter, the median filter , preserves edges much better than the mean filter. However, the median filter is effective in reducing discrete impulse noise, rather than smoothly generated noise. Furthermore, the median filter destroys thin lines and clips edges .

Still another type of filter is the sigma filter, which smoothes noise by averaging from a subset of the current window where all the pixels in the subset are from the same population. The subset is determined by a range that utilizes the standard deviation measured in that window multiplied by a t-parameter. By suitably

selecting the subset, it is possible to smooth out noise without degrading edge information. One problem that may occur with sigma filtering is that the subset determined by the calculated range may not necessarily include all the pertinent pixels for noise smoothing. Because of this, a larger range, which constitutes a larger t-parameter, is necessary to effectively smooth the noise. Unfortunately, by using a subset with a larger range, pixels that do not belong in the subset may be included.