二维和三维量子图像的存储、压缩与分割技术研究

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 project, three key technologies of quantum image processing are studied with the basic concept and principle of quantum computing, such as two-dimensional and three-dimensional quantum image storage, compression and segmentation. A two-dimensional or three-dimensional image will be represented by a quantum superposition state. And general quantum circuits will be designed to implement quantum image storage. Thus, the implementation of quantum storage has solved the first question of quantum image processing, which is "how to store an image in a quantum system", and is the basis and premise condition to process quantum images. Moreover, quantum image representation is as a compressed encoding and implements the classic compression of quantum images. Based on quantum image representation, the concept of quantum compression is proposed. Lossless and lossy quantum compression algorithm will be designed to implement quantum compression. A quantum segmentation algorithm based on a generalized Grover's algorithm will be proposed and be used in content-based image search. The research of the project is significant to the improvement of all aspects of image processing and 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.

量子计算是量子力学和计算机科学相结合的产物，作为一种新型的计算模式，已成为解决摩尔律失效问题的一个可能的解决方法。本项目结合量子计算的基本概念和原理，拟对量子图像处理技术中的二维和三维量子图像的存储、压缩与分割三个关键技术进行研究。本项目拟用一个量子叠加态表示一幅二维或三维图像，然后设计量子线路实现图像的量子存储，从而解决了量子图像处理的基础问题"如何将图像储存在量子系统"，为量子图像处理提供了前提条件和基础。同时，可将量子图像表示看成一种压缩编码，实现量子图像的经典压缩。在此基础上，提出量子压缩的概念，并分别设计无损和有损量子算法，实现量子图像的量子压缩。最后，设计基于推广的Grover搜索算法的量子图像分割算法，并将之应用到基于图像内容的搜索。本项目的研究有助于优化图像处理的各个环节，是量子计算理论在图像处理领域的拓展，对图像处理技术的发展和应用提供了一种新的观念和思路。

量子计算是量子力学和计算机科学相结合的产物，作为一种新型的计算模式，已成为解决摩尔律失效问题的一个可能的解决方法。本项目结合量子计算的基本概念和原理，对量子图像处理技术中的量子图像的存储、压缩与分割算法中的关键技术进行研究。首先，本项目用一个量子叠加态表示一幅二维或三维灰度和彩色图像，用一个量子比特存储灰度信息或彩色信息，并设计相应的量子线路实现从而实现了量子图像的高效压缩存储。其次，对量子图像的压缩技术进行研究，设计了多层Haar量子小波包变换和多层D(4)小波包变换的量子线路，从而补全了项目前期研究成果中量子图像压缩算法中缺少的核心工具算法；最后，对量子图像分割技术进行研究，提出了基于Sobel算子的量子图像边缘提取算法。本项目的研究是前期研究工作的扩展和深入，是量子计算理论在图像处理领域的拓展,有助于优化图像处理的各个环节，对图像处理技术的发展和应用提供了一种新的观念和思路。