A spectrum extrapolation method for image magnification

There are many kinds of interpolation methods to magnify an image. These methods proposed how to insert values between two neighbor values in an image. In general, a high-frequency band outside of a band-limitation cannot be obtained by using interpolation methods. Therefore a magnified image by an interpolation method blurs. This paper presents an extrapolation method to estimate high-frequency band theoretically. In the proposal method, we exploit the discrete Fourier transform (DFT) and the discrete Hilbert transform (DHT) in order to divide a frequency response into three components, a magnitude response, a minimum phase response and an all-pass phase response. These three responses are extrapolated respectively. Applying this method to an image, we can obtain a better image than that by using interpolation methods. By using a high pass filter, we verified that the obtained magnified image shaped the silhouette and had a spectrum in a high frequency band.