Fast Integer Sine and Cosine Transforms Type IV of Low Complexity for Video Coding

The matrix methods for constructing integer sine and cosine transforms type IV (IST-IV / ICT-IV) of orders 8 and 16 are proposed, based on which two integer transforms of type IV are constructed and fast algorithms for their calculation that only require operations with integers are developed. The a...

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Vydáno v:Cybernetics and systems analysis Ročník 61; číslo 2; s. 305 - 318
Hlavní autor: Hnativ, L. O.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.03.2025
Springer Nature B.V
Témata:
Algorithms
Artificial Intelligence
Complexity
Control
Integers
Mathematical programming
Mathematics
Mathematics and Statistics
Matrix
Matrix methods
Multiplication
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
Transformations (mathematics)
Trigonometric functions
discrete cosine transform
discrete sine transform
integer cosine transform
separable adaptive transform
MTS (Multiple Transform Selection)
H.265
video coding
factorization
VVC (Versatile Video Coding)
integer sine transform
ISSN:1060-0396, 1573-8337
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Shrnutí:The matrix methods for constructing integer sine and cosine transforms type IV (IST-IV / ICT-IV) of orders 8 and 16 are proposed, based on which two integer transforms of type IV are constructed and fast algorithms for their calculation that only require operations with integers are developed. The algorithms for calculating IST-IV/ ICT-IV of order 16 require, respectively, 14.29% and 12.5% fewer multiplication operations and 22.11% and 20.83% more addition operations compared to the known algorithms for discrete sine and cosine transforms type IV. The proposed fast IST-IV/ ICT-IV compared to the known fast discrete sine type VII and cosine type VIII transforms with integer approximation from the VVC standard (DST-VII/DCT-VIII) have 3.02 times less multiplicative complexity and require 47.41% fewer addition operations. Fast algorithms of low computational complexity for computing 2D separable integer cosine type II and sine type IV adaptive transforms for intra-prediction with image blocks have been developed, which have 2.66 times less multiplicative complexity and require 28.9% fewer addition operations compared to the known separable transforms ICT-II (H.265)/DST-VII (VVC).
Bibliografie:ObjectType-Article-1
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ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-025-00769-9