Vector transform and image coding

Vector transform-based OFDM

“…Although the VT was advanced in [9][10][11] FVT is generally computationally more complex than an FFT, it is should be noted that the FFT always requires complex arithmetic, while if the input to the VT is real (for example obtained as a result of BPSK modulation) and if the VT kernel is real, then the FVT requires only real arithmetic. In this case, assuming that M=2, the number of multiplications and additions for the FVT (4Nlog2 N and 6N log2 N) is actually lower than for the FFT ( 8N log2 (2N) and 8N log2 (2N) ).…”

“…First, suppose that {a1, ..., aM } are not necessarily distinct integers in the set {1,2, ..., N-1} for which gcd(ak, N) = 1. Then the diagonal matrix (10) satisfies conditions (8) and (9). Note that if V is a vector transform kernel (also called a seed), then if T is a unitary matrix, then W = TVT* is also a kernel.…”

“…VECTOR TRANSFORM The vector transform was advanced in [9][10][11]. The transform pair (7) where x[n] and X[k] are sequences of vectors of dimension Mxl1 constitute forward and inverse vector transform if the matrix kernel W of dimension MxM satisfies two conditions.…”

A study on orthogonal two-direction vector-valued wavelets and two-direction wavelet packets

“…Wavelets, which firstly succeed in the application and secondly form the theory, have been widely used in signal processing, image processing, quantum field theory, seismic exploration, voice recognition and synthesis, music, radar, CT imaging, color copies, fluid turbulence, object recognition, machine vision, machine fault diagnosis and monitoring, fractal and digital television, economic analysis and forecasting and so on [1][2][3][4][5][6][7][8][9][10]. Multiwavelets, which can offer properties like symmetry, orthogonality, short support at the same time, have been an active research field of wavelets analysis.…”

The Mallat Algorithm of Biorthogonal Two-direction Bivariate Wavelets and Application in Communication Engineering

“…It have been widely used in signal processing, image processing, voice recognition and synthesis, music, radar, machine fault diagnosis and monitoring, and so on [1][2][3][4][5][6]. Multiwavelets, which can offer properties as symmetry, orthogonality, short support at the same time, have been an active research field of wavelets analysis.…”