MOMENT-PRESERVING PIECEWISE-LINEAR APPROXIMATIONS OF SIGNALS AND IMAGES

Approximation techniques are an important aspect of digital signal and image processing. Many lossy signal compression procedures such as th e Fourier transform and discrete cosine transform are based on the ide a that a signal can be represented by a small number of transformed co efficients which are an approximation of the original. Existing approx imation techniques approach this problem in either a time/spatial doma in or transform domain, but not both. This paper briefly reviews vario us existing approximation techniques. Subsequently, we present a new s trategy to obtain an approximation (f) over cap(x) of f(x) in such a w ay that it is reasonably close to the original function in the domain of the variable x, and exactly preserves some properties of the transf ormed domain. In this particular case, the properties of the transform ed values that are preserved are geometric moments of the original fun ction. The proposed technique has been applied to single-variable func tions, two-dimensional planar curves, and two-dimensional images, and the results obtained are demonstrative.