Spectral extrapolation of spatially bounded images [MRI application]

A spectral extrapolation algorithm for spatially bounded images is presented. An image is said to be spatially bounded when it is confined to a closed region and is surrounded by a background of zeros. With prior 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 solution, has space variant resolution; features near the edge of the support region are better resolved than those in the center. The resolution of the finite support solution is discussed as a function of the number of known spatial zeros and known spectral components. A regularized version of the finite support solution is included for handling the case where the known spectral components are noisy. For both the noiseless and noisy cases, the resolution of the finite support solution is measured in terms of its impulse response characteristics, and compared to the resolution of the zerofilled and Nyquist solutions. The finite support solution is superior to the zerofilled solution for both the noisy and noiseless data cases. When compared to the Nyquist solution, the finite support solution may be preferred in the noisy data case. Examples using medical image data are provided.