Relaxed quaternionic Gabor expansions at critical density
نویسنده
چکیده
Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every continuous and quaternion-valued signal f in the Wiener space can be expanded into a unique `2 series on a lattice at critical density 1, provided one more point is added in the middle of a cell. We call that a relaxed Gabor expansion.
منابع مشابه
Nonharmonic Gabor Expansions
We consider Gabor systems generated by a Gaussian function and prove certain classical results of Paley and Wiener on nonharmonic Fourier series of complex exponentials for the Gabor expansion. In particular, we prove a version of Plancherel-Po ́lya theorem for entire functions with finite order of growth and use the Hadamard factorization theorem to study regularity, exactness and deficienc...
متن کاملQuaternionic gabor filters for local structure classification
We introduce quaternionic Gabor filters for the classification of local image structure. These filters are constructed as windowed basis functions of the quaternionic Fourier transform. We show that – in contrast to the 2D complex Gabor filters – the quaternionic Gabor filters are intrinsically 2D filters. A generalized phase concept is introduced and compared to the classical one. It is shown ...
متن کاملColor Face Recognition using Quaternionic Gabor Filters
While automated face recognition is a very important area of research and implementation, very few techniques make use of color information in recognition. However, both testing and analytic work indicate the potential advantages of using color. Existing work in Gabor filters for face recognition shows great promise, especially in robustness to illumination and pose variations. This proposed re...
متن کاملGabor and Wavelet Expansions
This paper is an examination of techniques for obtaining Fourier series-like expansions of finite-energy signals using so-called Gabor and wavelet expansions. These expansions decompose a given signal into time and frequency localized components. The theory of frames in Hilbert spaces is used as a criteria for determining when such expansions are good representations of the signals. Some result...
متن کاملMulti-Dimensional Signal Processin Using an Algebraically Extended Signal Representation
Many concepts that are used in multi{dimensional signal processing are derived from one{dimensional signal processing. As a consequence , they are only suited to multi{dimensional signals which are intrinsically one{dimensional. We claim that this restriction is due to the restricted algebraic frame used in signal processing, especially to the use of the complex numbers in the frequency domain....
متن کامل