Eigenstructures of spatial design matrices
Journal of Multivariate Analysis
A Steganographic Embedding Undetectable by JPEG Compatibility Steganalysis
IH '02 Revised Papers from the 5th International Workshop on Information Hiding
Capacity is the wrong paradigm
Proceedings of the 2002 workshop on New security paradigms
The discrete cosine transform DCT-4 and DCT-8
CompSysTech '03 Proceedings of the 4th international conference conference on Computer systems and technologies: e-Learning
On the discretization of nonparametric isotropic covariogram estimators
Statistics and Computing
Invariant spaces and cosine transforms DCT - 2 and DCT - 6
CompSysTech '04 Proceedings of the 5th international conference on Computer systems and technologies
A comrade-matrix-based derivation of the eight versions of fast cosine and sine transforms
Contemporary mathematics
Factorizations and representations of the backward second-order linear recurrences
Journal of Computational and Applied Mathematics
An improved preconditioned LSQR for discrete ill-posed problems
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
Harmonic Analysis of Finite Lamplighter Random Walks
Journal of Dynamical and Control Systems
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
Approximation by GP box-splines on a four-direction mesh
Journal of Computational and Applied Mathematics
Real-time fluid simulation using discrete sine/cosine transforms
Proceedings of the 2009 symposium on Interactive 3D graphics and games
Parallel preconditioners for large scale partial difference equation systems
Journal of Computational and Applied Mathematics
Linear filtering in DCT IV/DST IV and MDCT/MDST domain
Signal Processing
Convex Multi-class Image Labeling by Simplex-Constrained Total Variation
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
An upgraded petri net model, simulation and analysis of an 8Ũ8 sub-image for JPEG image compression
AIC'09 Proceedings of the 9th WSEAS international conference on Applied informatics and communications
Robust smoothing of gridded data in one and higher dimensions with missing values
Computational Statistics & Data Analysis
Algebraic signal processing theory: sampling for infinite and finite 1-D space
IEEE Transactions on Signal Processing
Bayesian classification using DCT features for brain tumor detection
KES'10 Proceedings of the 14th international conference on Knowledge-based and intelligent information and engineering systems: Part I
Antireflective boundary conditions for deblurring problems
Journal of Electrical and Computer Engineering - Special issue on iterative signal processing in communications
Finite difference discretization of the extended Fisher-Kolmogorov equation in two dimensions
Computers & Mathematics with Applications
Information Sciences: an International Journal
Nonparametric variogram and covariogram estimation with Fourier-Bessel matrices
Computational Statistics & Data Analysis
A Fast Algorithm for Fourier Continuation
SIAM Journal on Scientific Computing
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
Coupling Image Restoration and Segmentation: A Generalized Linear Model/Bregman Perspective
International Journal of Computer Vision
International Journal of Electronic Security and Digital Forensics
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Each discrete cosine transform (DCT) uses $N$ real basis vectors whose components are cosines. In the DCT-4, for example, the $j$th component of $\boldv_k$ is $\cos (j + \frac{1}{2}) (k + \frac{1}{2}) \frac{\pi}{N}$. These basis vectors are orthogonal and the transform is extremely useful in image processing. If the vector $\boldx$ gives the intensities along a row of pixels, its cosine series $\sum c_k \boldv_k$ has the coefficients $c_k=(\boldx,\boldv_k)/N$. They are quickly computed from a Fast Fourier Transform. But a direct proof of orthogonality, by calculating inner products, does not reveal how natural these cosine vectors are. We prove orthogonality in a different way. Each DCT basis contains the eigenvectors of a symmetric "second difference" matrix. By varying the boundary conditions we get the established transforms DCT-1 through DCT-4. Other combinations lead to four additional cosine transforms. The type of boundary condition (Dirichlet or Neumann, centered at a meshpoint or a midpoint) determines the applications that are appropriate for each transform. The centering also determines the period: $N-1$ or $N$ in the established transforms, $N-\frac{1}{2}$ or $N+ \frac{1}{2}$ in the other four. The key point is that all these "eigenvectors of cosines" come from simple and familiar matrices.