Image super‐resolution reconstruction using the high‐order derivative interpolation associated with fractional filter functions

Abstract

In this stydy, the authors present a single image super-resolution (SISR) reconstruction based on high-order derivative interpolation (HDI) in the fractional Fourier transform (FRFT) domain. First, the HDI formula is derived using a simple technique, which is based on the relationship between the fractional band-limited signal and the traditional band-limited signal. This interpolation formula contains the derivative information of the image and the FRFT domain filter functions (FDFF). Moreover, the advantages of the FDFF are also analysed. Second, the new SISR reconstruction is presented via the HDI. The main advantage is that the presented method involves the derivatives of an image in the resizing process. Moreover, the authors take advantage of the FDFF to resize the image. Furthermore, three evaluation criteria and some simulations are presented to validate the effectiveness of the proposed method. Last, the proposed method is applied to colour image processing. For a colour image case, the RGB colour space is chosen for super-resolution reconstruction. In addition to peak signal-to-noise ratio, the authors have also used the correlation to assess the quality of the reconstruction. Compared with many methods, extensive experimental results validate that the proposed method can obtain the better-edge characteristic, less blur and less aliasing.