Fundamentals of digital image processing
Fundamentals of digital image processing
Discrete-time signal processing
Discrete-time signal processing
Ten lectures on wavelets
An algorithm for computing a two-dimensional discrete Fourier transform of arbitrary order
Computational Mathematics and Mathematical Physics
Fourier-related transforms, fast algorithms and applications
Fourier-related transforms, fast algorithms and applications
Fast Algorithms for Digital Signal Processing
Fast Algorithms for Digital Signal Processing
Digital Image Processing
DFT/FFT and Convolution Algorithms: Theory and Implementation
DFT/FFT and Convolution Algorithms: Theory and Implementation
Fast Transforms: Algorithms, Analyses, Applications
Fast Transforms: Algorithms, Analyses, Applications
Orthogonal Transforms for Digital Signal Processing
Orthogonal Transforms for Digital Signal Processing
Split manageable efficient algorithm for Fourier and Hadamardtransforms
IEEE Transactions on Signal Processing
An algorithm for calculation of the discrete cosine transform by paired transform
IEEE Transactions on Signal Processing
Method of flow graph simplification for the 16-point discrete Fourier transform
IEEE Transactions on Signal Processing
2-D and 1-D multipaired transforms: frequency-time type wavelets
IEEE Transactions on Signal Processing
Shifted Fourier transform-based tensor algorithms for the 2-D DCT
IEEE Transactions on Signal Processing
Transform-based image enhancement algorithms with performance measure
IEEE Transactions on Image Processing
Method of paired transforms for reconstruction of images from projections: discrete model
IEEE Transactions on Image Processing
Signal Processing
On a Method of Paired Representation: Enhancement and Decomposition by Series Direction Images
Journal of Mathematical Imaging and Vision
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The analysis of the mathematical structure of the integral Fourier transform shows that the transform can be split and represented by certain sets of frequencies as coefficients of Fourier series of periodic functions in the interval $$[0,2\pi)$$. In this paper we describe such periodic functions for the one- and two-dimensional Fourier transforms. The approximation of the inverse Fourier transform by periodic functions is described. The application of the new representation is considered for the discrete Fourier transform, when the transform is split into a set of short and separable 1-D transforms, and the discrete signal is represented as a set of short signals. Properties of such representation, which is called the paired representation, are considered and the basis paired functions are described. An effective application of new forms of representation of a two-dimensional image by splitting-signals is described for image enhancement. It is shown that by processing only one splitting-signal, one can achieve an enhancement that may exceed results of traditional methods of image enhancement.