SPECTRAL EXTRAPOLATION OF SPATIALLY BOUNDED IMAGES

A spectral extrapolation algorithm for spatially bounded images is pre sented, An image is said to be spatially bounded when it is confined t o a closed region and is surrounded by a background of zeros. With pri or knowledge of the spatial domain zeros, the extrapolation algorithm extends the image's spectrum beyond a known interval of low-frequency components, The result, which is referred to as the finite support sol ution, has space variant resolution; features near the edge of the sup port region are better resolved than those in the center, The resoluti on of the finite support solution is discussed as a function of the nu mber of known spatial zeros and known spectral components, A regulariz ed version of the finite support solution is included for handling the case where the known spectral components are noisy, For both the nois eless and noisy cases, the resolution of the finite support solution i s measured in terms of its impulse response characteristics, and compa red to the resolution of the zerofilled and Nyquist solutions. The fin ite support solution is superior to the zerofilled solution for both t he noisy and noiseless data cases, When compared to the Nyquist soluti on, the finite support solution may be preferred in the noisy data cas e. Examples using medical image data are provided.