Gabor Function

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform

J R Williamson - One of the best experts on this subject based on the ideXlab platform.

Isao Hayashi - One of the best experts on this subject based on the ideXlab platform.

Giorgio Bonmassar - One of the best experts on this subject based on the ideXlab platform.

  • dual energy pulses for electrical impedance spectroscopy with the stochastic Gabor Function
    International Conference of the IEEE Engineering in Medicine and Biology Society, 2012
    Co-Authors: Giorgio Bonmassar, Maria Ida Iacono, Michael H Lev
    Abstract:

    This paper introduces the stochastic Gabor Function (SGF), an excitation waveform that can be used to design optimal excitation pulses for Electrical Impedance Spectroscopy (EIS) of the brain. The SGF is a Gaussian Function modulated by uniformly distributed noise; it has wide frequency spectrum representation regardless of the stimuli pulse length. The SGF was studied in the time-frequency domain. As shown by frequency concentration measurements, the SGF is least compact in the sample frequency phase plane. Numerical results obtained by using a realistic human head model indicate that the SGF may allow for both shallow and deeper tissue penetration than is currently obtainable with conventional stimulus paradigms, potentially facilitating tissue subtraction assessment of parenchymal dielectric changes in frequency. This could be of value in advancing EIS of stroke and hemorrhage.

  • EMBC - Dual energy pulses for Electrical Impedance Spectroscopy with the stochastic Gabor Function
    Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Inte, 2012
    Co-Authors: Giorgio Bonmassar, Maria Ida Iacono, Michael H Lev
    Abstract:

    This paper introduces the stochastic Gabor Function (SGF), an excitation waveform that can be used to design optimal excitation pulses for Electrical Impedance Spectroscopy (EIS) of the brain. The SGF is a Gaussian Function modulated by uniformly distributed noise; it has wide frequency spectrum representation regardless of the stimuli pulse length. The SGF was studied in the time-frequency domain. As shown by frequency concentration measurements, the SGF is least compact in the sample frequency phase plane. Numerical results obtained by using a realistic human head model indicate that the SGF may allow for both shallow and deeper tissue penetration than is currently obtainable with conventional stimulus paradigms, potentially facilitating tissue subtraction assessment of parenchymal dielectric changes in frequency. This could be of value in advancing EIS of stroke and hemorrhage.

  • The Stochastic Gabor Function Enhances Bandwidth In Finite-Difference-Time Domain $S$ -Parameter Estimation
    IEEE Transactions on Microwave Theory and Techniques, 2007
    Co-Authors: Giorgio Bonmassar
    Abstract:

    This paper introduces the stochastic Gabor Function, an excitation waveform that can be used for finite-difference time-domain S-parameter estimation. The stochastic Gabor Function is a Gaussian Function modulated by uniformly distributed noise; it has wide frequency spectrum representation regardless of the stimuli pulse length. The stochastic Gabor Function was studied in the time-frequency domain and was compared to Gaussian and Gabor stimuli Functions with the same length. As shown by frequency concentration measurements, the stochastic Gabor Function is least compact in the sample frequency phase plane. Numerical results obtained by using a multilayer stripline indicate that the stochastic Gabor Function provides convergence and stability similar to those provided by the Gabor and Gaussian Functions, but produces a much wider frequency band response when used as a pointwise hard voltage source stimulus

Michael Unser - One of the best experts on this subject based on the ideXlab platform.

  • construction of hilbert transform pairs of wavelet bases and Gabor like transforms
    arXiv: Information Theory, 2009
    Co-Authors: Kunal Narayan Chaudhury, Michael Unser
    Abstract:

    We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling Functions--the B-spline factorization theorem. In particular, starting from well-localized scaling Functions, we construct HT pairs of biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor Function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for constructing 2D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1D counterpart, we relate the real and imaginary components of these complex wavelets using a multi-dimensional extension of the HT--the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor Functions proposed by Daugman. Finally, we present an efficient FFT-based filterbank algorithm for implementing the associated complex wavelet transform.

  • Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms
    IEEE Transactions on Signal Processing, 2009
    Co-Authors: Kunal Narayan Chaudhury, Michael Unser
    Abstract:

    We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling Functions-the B-spline factorization theorem. In particular, starting from well-localized scaling Functions, we construct HT pairs of biorthogonal wavelet bases of L2(R) by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor Function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of L2(R2), we then discuss a methodology for constructing 2-D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1-D counterpart, we relate the real and imaginary components of these complex wavelets using a multidimensional extension of the HT-the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor Functions proposed by Daugman. Finally, we present an efficient fast Fourier transform (FFT)-based filterbank algorithm for implementing the associated complex wavelet transform.

Giovanna Citti - One of the best experts on this subject based on the ideXlab platform.

  • A sub-Riemannian model of the visual cortex with frequency and phase
    The Journal of Mathematical Neuroscience, 2020
    Co-Authors: Emre Baspinar, Alessandro Sarti, Giovanna Citti
    Abstract:

    In this paper, we present a novel model of the primary visual cortex (V1) based on orientation, frequency, and phase selective behavior of V1 simple cells. We start from the first-level mechanisms of visual perception, receptive profiles. The model interprets V1 as a fiber bundle over the two-dimensional retinal plane by introducing orientation, frequency, and phase as intrinsic variables. Each receptive profile on the fiber is mathematically interpreted as rotated, frequency modulated, and phase shifted Gabor Function. We start from the Gabor Function and show that it induces in a natural way the model geometry and the associated horizontal connectivity modeling of the neural connectivity patterns in V1. We provide an image enhancement algorithm employing the model framework. The algorithm is capable of exploiting not only orientation but also frequency and phase information existing intrinsically in a two-dimensional input image. We provide the experimental results corresponding to the enhancement algorithm.

  • A sub-Riemannian model of the visual cortex with frequency and phase
    2019
    Co-Authors: Emre Baspinar, Alessandro Sarti, Giovanna Citti
    Abstract:

    In this paper we present a novel model of the primary visual cortex (V1) based on orientation, frequency and phase selective behavior of the V1 simple cells. We start from the first level mechanisms of visual perception: receptive profiles. The model interprets V1 as a fiber bundle over the 2-dimensional retinal plane by introducing orientation, frequency and phase as intrinsic variables. Each receptive profile on the fiber is mathematically interpreted as a rotated, frequency modulated and phase shifted Gabor Function. We start from the Gabor Function and show that it induces in a natural way the model geometry and the associated horizontal connectivity modeling the neural connectivity patterns in V1. We provide an image enhancement algorithm employing the model framework. The algorithm is capable of exploiting not only orientation but also frequency and phase information existing intrinsically in a 2-dimensional input image. We provide the experimental results corresponding to the enhancement algorithm.

  • A Geometric Model of Multi-scale Orientation Preference Maps via Gabor Functions
    Journal of Mathematical Imaging and Vision, 2018
    Co-Authors: Emre Baspinar, Giovanna Citti, Alessandro Sarti
    Abstract:

    In this paper we present a new model for the generation of orientation preference maps in the primary visual cortex (V1), considering both orientation and scale features. First we undertake to model the Functional architecture of V1 by interpreting it as a principal fiber bundle over the 2-dimensional retinal plane by introducing intrinsic variables orientation and scale. The intrinsic variables constitute a fiber on each point of the retinal plane and the set of receptive profiles of simple cells is located on the fiber. Each receptive profile on the fiber is mathematically interpreted as a rotated Gabor Function derived from an uncertainty principle. The visual stimulus is lifted in a 4-dimensional space, characterized by coordinate variables, position, orientation and scale, through a linear filtering of the stimulus with Gabor Functions. Orientation preference maps are then obtained by mapping the orientation value found from the lifting of a noise stimulus onto the 2-dimensional retinal plane. This corresponds to a Bargmann transform in the reducible representation of the $$\text {SE}(2)=\mathbb {R}^2\times S^1$$ SE ( 2 ) = R 2 × S 1 group. A comparison will be provided with a previous model based on the Bargmann transform in the irreducible representation of the $$\text {SE}(2)$$ SE ( 2 ) group, outlining that the new model is more physiologically motivated. Then, we present simulation results related to the construction of the orientation preference map by using Gabor filters with different scales and compare those results to the relevant neurophysiological findings in the literature.

  • A geometric model of multi-scale orientation preference maps via Gabor Functions
    arXiv: Neurons and Cognition, 2017
    Co-Authors: Emre Baspinar, Giovanna Citti, Alessandro Sarti
    Abstract:

    In this paper we present a new model for the generation of orientation preference maps in the primary visual cortex (V1), considering both orientation and scale features. First we undertake to model the Functional architecture of V1 by interpreting it as a principal fiber bundle over the 2-dimensional retinal plane by introducing intrinsic variables orientation and scale. The intrinsic variables constitute a fiber on each point of the retinal plane and the set of receptive profiles of simple cells is located on the fiber. Each receptive profile on the fiber is mathematically interpreted as a rotated Gabor Function derived from an uncertainty principle. The visual stimulus is lifted in a 4-dimensional space, characterized by coordinate variables, position, orientation and scale, through a linear filtering of the stimulus with Gabor Functions. Orientation preference maps are then obtained by mapping the orientation value found from the lifting of a noise stimulus onto the 2-dimensional retinal plane. This corresponds to a Bargmann transform in the reducible representation of the $\text{SE}(2)=\mathbb{R}^2\times S^1$ group. A comparison will be provided with a previous model based on the Bargman transform in the irreducible representation of the $\text{SE}(2)$ group, outlining that the new model is more physiologically motivated. Then we present simulation results related to the construction of the orientation preference map by using Gabor filters with different scales and compare those results to the relevant neurophysiological findings in the literature.

Related terms

Gabor Function - 15 days free trial to Access Experts & Abstracts