Key Techniques Research On Quantum Image Processing

Quantum computing is the combination of quantum mechanics and computer science. As a new computing paradigm, it becomes one possible solution to the problem posed by the failure of Moore’s law. In this paper, four key technologies of quantum image processing are studied with the basic concept and principle of quantum computing, such as image storage and retrieval, image geometry transform, image compression and image segmentation. On the one hand, as the technology reserve of theories and methods for the future quantum computer, the research on quantum image processin is significant to the improvement of the theory and the promotion of applicationthe of quantum computing. On the other hand, the research on quantum image processing is also the expansion of quantum computing theory in image processing field, providing a new idea for the development and application of image processing technology. The outlines and contributions of this dissertation are summarized as follows:1. Five methods of quantum image representation based on a single qubit state or a multiple qubit state are proposed and listed as follows: Single qubit states for an image, a Normal Arbitrary Superposition State(NASS) for a multidimensional image, a Normal Arbitrary Quantum Superposition State(NAQSS) for a multidimensional image and some additional information, a normal arbitrary superposition state with relative phases(NASSRP) for a multidimensional image and some additional information, a Normal Arbitrary Superposition State with Three Components(NASSTC) for a multidimensional color image. We also design five general quantum circuits and the corresponding image retrieval schemes for the five methods of quantum image representation, respectively. The implementations of quantum storage and retrieval have solved the first question of quantum image processing, which is “how to store an image in a quantum system and retrieve it”, and are the basis and premise condition to process quantum images.2. Some geometric transformation operators of multidimensional quantum color image based on NASS are presented, including two-point swapping, symmetric flip, local flip, orthogonal rotation and translation transform. Moreover, these geometric transformation operators are implemented by quantum circuits. By analyzing the complexities of quantum circuits, we conclude that geometric transformation operators based on NASS can be implemented efficiently.3. Two kinds of quantum image compression(i.e., classical compression and quantum compression of quantum image) are studied. Classical compression of quantum image reduces the redundant data to economize the memory resources. Quantum compression of quantum image reduces the number of items whose coefficients are zero in a superposition state to decrease the resources required to implement quantum image storage and operation. For the first time, we implement the quantum compression of multidimensional quantum color images. Thus, we address the theoretical and practical aspects of image processing on a quantum computer.4. A quantum segmentation algorithm based on a generalized Grover’s algorithm is proposed. The initial state of the generalized Grover’s algorithm is the NAQSS state, which stores a multidimensional image and some segmentation information. According to the statistics information of the initial image, the appropriate phase rotation angle and the number of iterations are selected to search out marked states(i.e., target objects in the image) with the minimum number of iterations and the maximum probability. Thus, quantum image segmentation is implemented. The quantum segmentation algorithm based on a generalized Grover’s algorithm is also a new scheme to implement content-based image search.