Integer multiple quantum image scaling based on NEQR and bicubic interpolation

Abstract

As a branch of quantum image processing, quantum image scaling has been widely studied. However, most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation, the quantum version of bicubic interpolation has not yet been studied. In this work, we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation (NEQR). Our scheme can realize synchronous enlargement and reduction of the image with the size of 2 n × 2 n by integral multiple. Firstly, the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules. Then, 16 neighborhood pixels are obtained by quantum operation circuits, and the corresponding weights of these pixels are calculated by quantum arithmetic modules. Finally, a quantum matrix operation, instead of a classical convolution operation, is used to realize the sum of convolution of these pixels. Through simulation experiments and complexity analysis, we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm, and has better effect than the quantum version of bilinear interpolation.