New look on quantum representation of images: Fourier transform representation

摘要

Image representation plays an essential role in quantum image processing and quantum computer vision in numerous, computationally expensive applications. Quantum image processing is a new discipline with tremendous potential. However, there is a critical problem in applying quantum computing to process data: how to represent data (signal, image, and video data) using quantum states without losing information. In this paper, we describe briefly a few known models for image representation and propose a new approach for representing discrete signals and images in quantum computing, by mapping the input data into the unit circle, or only part of the circle. Such a representation allows for introducing the concept of the Fourier transform qubit representation. For grayscale images, we consider the similar concept of the Fourier representation of images and, for color images, we introduce models with the concept of the 3-point DFT of color qubits. The circuits for proposed signal and image representations are described.