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Quantum Discrete Cosine Transform for Image Compression

Chao Yang Pang·Zheng Wei Zhou·Guang Can Guo
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Abstract

Discrete Cosine Transform (DCT) is very important in image compression. Classical 1-D DCT and 2-D DCT has time complexity O(NlogN) and O(N²logN) respectively. This paper presents a quantum DCT iteration, and constructs a quantum 1-D and 2-D DCT algorithm for image compression by using the iteration. The presented 1-D and 2-D DCT has time complexity O(sqrt(N)) and O(N) respectively. In addition, the method presented in this paper generalizes the famous Grover's algorithm to solve complex unstructured search problem.

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Chao Yang Pang, Zheng Wei Zhou, Guang Can Guo. 2006-01-22. Quantum Discrete Cosine Transform for Image Compression. https://arxiv.org/abs/quant-ph/0601043

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