SIAM Journal on Scientific and Statistical Computing
Multiplicative complexity, convolution, and the DFT
Multiplicative complexity, convolution, and the DFT
Discrete cosine transform: algorithms, advantages, applications
Discrete cosine transform: algorithms, advantages, applications
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Image and Video Compression Standards: Algorithms and Architectures
Image and Video Compression Standards: Algorithms and Architectures
JPEG Still Image Data Compression Standard
JPEG Still Image Data Compression Standard
IEEE Transactions on Computers
Efficient hybrid DCT-domain algorithm for video spatial downscaling
EURASIP Journal on Advances in Signal Processing
A non-probabilistic recognizer of stochastic signals based on KLT
Signal Processing
GNU Octave Manual Version 3
A Matrix Handbook for Statisticians
A Matrix Handbook for Statisticians
Nonlinear system identification: an effective framework based on the Karhunen-Loève transform
IEEE Transactions on Signal Processing
Fast algorithms for the discrete cosine transform
IEEE Transactions on Signal Processing
Fast multiplierless approximations of the DCT with the liftingscheme
IEEE Transactions on Signal Processing
The Distributed Karhunen–Loève Transform
IEEE Transactions on Information Theory
The JPEG still picture compression standard
IEEE Transactions on Consumer Electronics
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
Introduction to the special issue on the H.264/AVC video coding standard
IEEE Transactions on Circuits and Systems for Video Technology
Overview of the H.264/AVC video coding standard
IEEE Transactions on Circuits and Systems for Video Technology
Scalable variable complexity approximate forward DCT
IEEE Transactions on Circuits and Systems for Video Technology
An Effective Classification Framework for Brain–Computer Interfacing Based on a Combinatoric Setting
IEEE Transactions on Signal Processing
Asynchronous realization of algebraic integer-based 2D DCT using achronix speedster SPD60 FPGA
Journal of Control Science and Engineering - Special issue on Hardware Implementation of Digital Signal Processing Algorithms
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The discrete cosine transform (DCT) is a central mathematical operation in several digital signal processing methods and image/video standards. In this paper, we propose a collection of twelve approximations for the 8-point DCT based on integer functions. Considered functions include: the floor, ceiling, truncation, and rounding-off functions. Sought approximations are required to meet the following specific criteria: (i) very low arithmetic complexity, (ii) orthogonality or quasi-orthogonality, and (iii) low-complexity inversion. By varying a scaling parameter, approximations could be systematically obtained and several existing approximations were identified as particular cases of the proposed methodology. Particular cases include the signed DCT and the rounded DCT. Four new quasi-orthogonal approximations were introduced and their practical relevance was demonstrated. All approximations were given fast algorithms based on matrix factorization methods. Proposed approximations are multiplierless; their computation requires only additions and bit-shifting operations. Additive complexity ranged from 18 to 24 additions. Obtained approximations were compared with the exact DCT and assessed in the context of JPEG-like image compression. As quality assessment measures, we considered the peak signal-to-noise ratio and the structural similarity index. Because its low-complexity and good performance properties, the proposed approximations are suitable for hardware implementation in dedicated architectures.