Quantum Discrete Cosine Transform for Image Compression

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.

[1]  庞朝阳,et al.  Design of quantum VQ iteration and quantum VQ encoding algorithm taking O(N1/2) steps for data compression , 2006 .

[2]  G. Long.  Grover algorithm with zero theoretical failure rate , 2001, quant-ph/0106071.

[3]  A. Klappenecker,et al.  Discrete cosine transforms on quantum computers , 2001, ISPA 2001. Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis. In conjunction with 23rd International Conference on Information Technology Interfaces (IEEE Cat..

[4]  Prof. Dr. Thomas Bräunl,et al.  Parallel Image Processing , 2001, Springer Berlin Heidelberg.

[5]  José Ignacio Latorre,et al.  Image compression and entanglement , 2005, ArXiv.

[6]  Sun Yang.  Phase Matching in Quantum Searching and the Improved Grover Algorithm , 2004 .

[7]  William Stallings.  Computer Organization and Architecture , 2002 .

[8]  Gilles Brassard,et al.  Tight bounds on quantum searching , 1996, quant-ph/9605034.

[9]  U. Toronto,et al.  Analysis of generalized Grover quantum search algorithms using recursion equations , 2000, quant-ph/0010077.

[10]  A. Galindo,et al.  Information and computation: Classical and quantum aspects , 2001, quant-ph/0112105.

[11]  Markus Grassl,et al.  Grover's quantum search algorithm for an arbitrary initial amplitude distribution , 1999 .

[12]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[13]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.