Edge feature enhancement approach using hilbert transform of Cauchy distribution and its applications

Abstract In this paper, we introduced an efficient inversion method for Hilbert transform calculation which can be able to eliminate the outlier noise. The Most Frequent Value method (MFV) developed by Steiner merged with an inversion-based Fourier transform to introduce a powerful Fourier transform. The Fourier transform process (IRLS-FT) ability to noise overthrow efficiency and refusal to outliers make it an applicable method in the field of seismic data processing. In the first part of the study, we introduced the Hilbert transform stand on a efficient inversion, after that as an example we obtain the absolute value of the analytical signal which can be used as an attribute gauge. The method depends on a dual inversion, first we obtain the Fourier spectrum of the time signal via inversion, after that, the spectrum calculated via transformation of Hilbert transforms into time range using a efficient inversion. Steiner Weights is used later and calculated using the Iterative Reweighting Least Squares (IRLS) method (efficient inverse Fourier transform). Hermite functions in a series expansion are used to discretize the spectrum of the signal in time. These expansion coefficients are the unknowns in this case. The test procedure was made on a Ricker wavelet signal loaded with Cauchy distribution noise to test the new Hilbert transform. The method shows very good resistance to outlier noises better than the conventional (DFT) method.

Download Full-text

Time Statistics of Heart Beat Intervals and Cauchy Distribution

PsycEXTRA Dataset ◽

10.1037/e539142010-001 ◽

2003 ◽

Author(s):

M. Martinis ◽

A. Knezevic

Keyword(s):

Cauchy Distribution ◽

Heart Beat

Download Full-text

Model of multicomponent narrow-band periodical non-stationary random signal

Information extraction and processing ◽

10.15407/vidbir2020.48.017 ◽

2020 ◽

Vol 2020 (48) ◽

pp. 17-24

Author(s):

I.M. Javorskyj ◽

◽

R.M. Yuzefovych ◽

P.R. Kurapov ◽

◽

...

Keyword(s):

Time Series ◽

Real Time ◽

Hilbert Transform ◽

Spectral Properties ◽

Narrow Band ◽

Analytic Signal ◽

Random Signal ◽

Hilbert Transformation ◽

The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

Download Full-text

A Bayesian View on the Hilbert Transform and the Kramers-Kronig Transform of Electrochemical Impedance Data: Probabilistic Estimates and Quality Scores

10.26434/chemrxiv.12152529 ◽

2020 ◽

Cited By ~ 1

Author(s):

Jiapeng Liu ◽

Ting Hei Wan ◽

Francesco Ciucci

Keyword(s):

Power Generation ◽

Electrochemical Impedance Spectroscopy ◽

Hilbert Transform ◽

Electrochemical Impedance ◽

The Self ◽

Impedance Data ◽

The Hilbert Transform ◽

Validation Tests ◽

Self Consistency ◽

Mathematical Relations

<p>Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental tools in electrochemistry and has applications ranging from energy storage and power generation to medicine. Considering the broad applicability of the EIS technique, it is critical to validate the EIS data against the Hilbert transform (HT) or, equivalently, the Kramers–Kronig relations. These mathematical relations allow one to assess the self-consistency of obtained spectra. However, the use of validation tests is still uncommon. In the present article, we aim at bridging this gap by reformulating the HT under a Bayesian framework. In particular, we developed the Bayesian Hilbert transform (BHT) method that interprets the HT probabilistic. Leveraging the BHT, we proposed several scores that provide quick metrics for the evaluation of the EIS data quality.<br></p>

Download Full-text