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Quantum Information Processing

NEQR: a novel enhanced quantum representation of digital images

Yi Zhang, Kai Lü, Yinghui Gao, Mo Wang

Published Mar 25, 2013• 732 citations
Publisher
DOI
10.1007/s11128-013-0567-z

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Quantum image representation plays an important role in quantum image processing. In this paper, a bitplane representation of quantum images (BRQI) is proposed, which uses (n+4) or (n+6) qubits to store a grayscale or RGB color image of 2npixels. Compared with a novel enhanced quantum representation (NEQR), and a novel quantum representation of color digital images (NCQI), the storage capacity of BRQI improves 16 times and 218times, respectively. Next, some quantum operations based on BRQI are proposed, these operations including complement of colors, reverse of bitplanes, and translation of bitplanes. Analyzed the implementation circuits of these operations, the result indicates that these operations based on BRQI have lower quantum cost than NEQR and NCQI. Furthermore, an image scrambling algorithm based on BRQI is presented by combining the above operations. Simulation experiments and performance analysis show that proposed scrambling algorithm is effective and efficient.
We present, QBMR (Quantum Bipartite Minterm Representation), a novel quantum representation of digital images. The representation is based on the one-to-one correspondence between digital images and bipartite graphs. The qubit cost of QBMR is logarithmic in the size of the image and linear in the pixel depth of the image. We observe that that QBMR yields significantly smaller circuit sizes when compared to similar image representation schemes. We present comparative data with the Novel Enhanced Quantum Representation (NEQR) for circuit sizes. Finally, QBMR allows for the use of Boolean function analysis techniques to be introduced into domain of Quantum Image Processing.