Low-Complexity Scaling Methodsfor DCT-II Approximations

This paper introduces a collection of scaling methods for generating \text{2}\,N-point DCT-II approximations based on N-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact \text{2}\,N-point DCT-II matrix. Encompassing the widely employed...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2021, Vol.69, p.4557-4566
Main Authors: Coelho, Diego, Cintra, Renato, Madanayake, Arjuna, Perera, Sirani
Format: Article
Language:English
Subjects:
Approximation
Approximation algorithms
approximations
Complexity
Discrete cosine transform
Discrete cosine transforms
Error analysis
Hardware
Image coding
Matrix decomposition
Orthogonality
Scaling
Transforms
Video compression
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Summary:This paper introduces a collection of scaling methods for generating \text{2}\,N-point DCT-II approximations based on N-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact \text{2}\,N-point DCT-II matrix. Encompassing the widely employed Jridi-Alfalou-Meher scaling method, the proposed techniques are shown to produce DCT-II approximations that outperform the transforms resulting from the JAM scaling method according to total error energy and mean squared error. Orthogonality conditions are derived and an extensive error analysis based on statistical simulation demonstrates the good performance of the introduced scaling methods. A hardware implementation is also provided demonstrating the competitiveness of the proposed methods when compared to the JAM scaling method.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2021.3099623