Paper Info
Title
Signal and image compression using quantum discrete cosine transform.
Abstract
The discrete cosine transform (DCT) is widely used in image and video compression standard formats. This is due to its ability to represent signals and images using a limited number of significant coefficients without noticeable loss of visual clarity. The classical one-dimensional discrete cosine transform (1D - DCT) and two-dimensional discrete cosine transform (2D - DCT) have computational complexities of O(Nlog2N) and O(N2log2N), respectively. Thus, as the images grow in size, the runtime of the DCT highly increases which could limit its usability in real-time applications. This paper presents a quantum DCT algorithm (QDCT) that is more efficient than its classical counterpart in terms of complexity. Furthermore, the proposed QDCT is used to develop and realize a quantum image compression technique. The developed compression technique performs a search to determine the most significant computed DCT coefficients and is derived from Grover’s algorithm. It provides a generalization to the original search algorithm by utilizing two oracle operators to solve the complex unstructured search problem rather than a single one. Thus, the proposed QDCT algorithm can simultaneously calculate the DCT coefficients and identify the significant DCT coefficients through applying two oracles. The comparison of the introduced QDCT with Grover’s algorithm also indicates that the QDCT algorithm is more efficient. This can be attributed to performing a rotation on the subspace rather than on the global space in Grover’s algorithm. In addition, the presented quantum 1D - and 2D - DCT have reduced complexities compared to the classical algorithms which are O(N) and O(N), respectively. Therefore, the presented QDCT and compression algorithm can be applied efficiently to accomplish various transform-based quantum signal and image processing tasks.
Year
DOI
Venue
2019
10.1016/j.ins.2018.08.067
Information Sciences
Keywords
Field
DocType
Discrete cosine transformation,Quantum mechanics,Signal and image processing,Image compression,Grover’S algorithm
Discrete mathematics,Search algorithm,Subspace topology,Discrete cosine transform,Image processing,Algorithm,Oracle,Search problem,Data compression,Mathematics,Image compression
Journal
Volume
ISSN
Citations 
473
0020-0255
3
PageRank 
References 
Authors
0.37
14
5
Name
Order
Citations
PageRank
Chao-yang Pang1347.10
Ri-Gui Zhou2138.29
Benqiong Hu3296.16
Wenwen Hu4406.85
Ahmed El-Rafei593.18