Two-dimensional image zooming by adaptive Sinc-based technique

Abstract

This article reports a novel adaptive Sinc-based zooming technique. The theoretical basis of the zooming technique is the Whittaker–Shannon interpolation formula and the Nyquist–Shannon sampling theorem. The technique can be used to zoom out, zoom in, and reconstruct two-dimensional images with no zoom. The technique introduces a novel concept called pixel-local-scaled k-space, which is calculated as follows. The k-space magnitude and the bandwidth of the image to zoom are calculated. The bandwidth of the frequency components of the image to zoom is estimated by the difference between the maximum and the minimum numerical value of the k-space magnitude. The ratio between the standardised k-space magnitude of the image and the bandwidth is calculated pixel-by-pixel, and is called pixel-local-scaled k-space. The signal is reconstructed using a finite convolution between image pixel intensities and Sinc functions. The zooming factor is consequential to the numerical difference between the pixel-local-scaled k-space and the sampling rate. The novelty of this zooming technique is to be adaptive because the pixel-local-scaled k-space is a pixel-by-pixel map, that is, an image with the same number of pixels as the departing image. Adaptive Sinc-based zooming is validated through the comparison with non-adaptive Sinc-based zooming, and its smoothing effect is compared to the smoothing of a variety of image space and z-space filters. The adaptive Sinc-based zooming technique achieves image zooming reconstruction using sampling rates within an extended range versus the range allowed by non-adaptive Sinc-based zooming.