Optimal discrete wavelet design for cardiac signal processing

Karel, Joël; Peeters, Ralf; Westra, Ronald L.; Moermans, K.M.S.; Haddad, S.A.P.; Serdijn, Wouter A.

doi:10.1109/iembs.2005.1617046

Cited by 32 publications

(41 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(b) Maximization of the variance of the sequence of energies | | is equivalent to maximization of the "L4-norm" ∑ | | . The proof of this theorem can be found in [25].…”

Section: Methodology 31 Criteria For Wavelet Designmentioning

confidence: 99%

“…Criteria 1&2: A guiding principle proposed there was to aim for maximization of the variance, either maximization of the variance of the absolute values of the wavelet coefficients, or maximization of the variance of the squared wavelet coefficients i.e. of the energy distribution over the wavelet contributions at the various scales [25]. The theorem presented in [25] is as follow:…”

Section: Methodology 31 Criteria For Wavelet Designmentioning

confidence: 99%

“…of the energy distribution over the wavelet contributions at the various scales [25]. The theorem presented in [25] is as follow:…”

Section: Methodology 31 Criteria For Wavelet Designmentioning

confidence: 99%

“…Two criteria based on this cost function can be presented as follow [25]. Criteria 1&2: A guiding principle proposed there was to aim for maximization of the variance, either maximization of the variance of the absolute values of the wavelet coefficients, or maximization of the variance of the squared wavelet coefficients i.e.…”

Section: Methodology 31 Criteria For Wavelet Designmentioning

confidence: 99%

“…Then [25]: (a) Maximization of the variance of the sequence of absolute values | |is equivalent to minimization of the "L1-norm" ∑ | | . (b) Maximization of the variance of the sequence of energies | | is equivalent to maximization of the "L4-norm" ∑ | | .…”

Section: Methodology 31 Criteria For Wavelet Designmentioning

confidence: 99%

See 4 more Smart Citations

Improved Denoising Method for Ultrasonic Echo with Mother Wavelet Optimization and Best-Basis Selection

Mohammadi¹

2016

IJECE

View full text Add to dashboard Cite

Weak features of ultrasonicnondestructive test signals are usually immersed in noisy signals. So, in this paper, we proposed an improved scheme for noise reduction and feature extraction based on discrete wavelet transform. The basis of the mother wavelet was selected to be matched to a given signal. Three different constraints were presented to minimize the error between the denoised and the given signal. It should be mentioned that such an optimum wavelet can represent the signal more compactly with a few large coefficients which can be considered as the signal features. Standard signals and simulated ultrasonic echo were used to evaluate the performance of the presented algorithms. Signal to error ratio was used to compare the designed wavelet performance with that of standard wavelets. Simulation results revealed that the proposed method outperformed the other presented methods and even standard wavelets. The results also has shown that the signal-based noise reduction algorithms make the feature extraction more reliable. Finally, the performance of the proposed algorithm was compared with other methods from different literatures. Keyword:Denoising Discrete wavelet transform Threshold Ultrasonic_NDT

show abstract

“…(b) Maximization of the variance of the sequence of energies | | is equivalent to maximization of the "L4-norm" ∑ | | . The proof of this theorem can be found in [25].…”

Section: Methodology 31 Criteria For Wavelet Designmentioning

confidence: 99%

Section: Methodology 31 Criteria For Wavelet Designmentioning

confidence: 99%

“…of the energy distribution over the wavelet contributions at the various scales [25]. The theorem presented in [25] is as follow:…”

Section: Methodology 31 Criteria For Wavelet Designmentioning

confidence: 99%

Section: Methodology 31 Criteria For Wavelet Designmentioning

confidence: 99%

Section: Methodology 31 Criteria For Wavelet Designmentioning

confidence: 99%

See 3 more Smart Citations

Improved Denoising Method for Ultrasonic Echo with Mother Wavelet Optimization and Best-Basis Selection

Mohammadi¹

2016

IJECE

View full text Add to dashboard Cite

show abstract

Analog Wavelet Filters: The Need for Approximation

Haddad¹,

Serdijn

2009

Ultra Low-Power Biomedical Signal Processing

View full text Add to dashboard Cite

Orthogonal Matched Wavelets with Vanishing Moments: A Sparsity Design Approach

Karel

Peeters

2017

Circuits Syst Signal Process

View full text Add to dashboard Cite

This paper presents a novel approach to design orthogonal wavelets matched to a signal with compact support and vanishing moments. It provides a systematic and versatile framework for matching an orthogonal wavelet to a specific signal or application. The central idea is to select a wavelet by optimizing a criterion which promotes sparsity of the wavelet representation of a prototype signal. Optimization is performed over the space of orthogonal wavelet functions with compact support, coming from filter banks with a given order. Parametrizations of this space are accompanied by explicit conditions for extra vanishing moments, to be used for constrained optimization. The approach is developed first for critically sampled wavelet transforms, then for undecimated wavelet transforms. Two different optimization criteria are presented: to achieve sparsity by L 1 -minimization or by L 4 -norm maximization. Masking can be employed by introducing weighting factors. Examples are given to demonstrate and evaluate the approach.

show abstract

Optimal discrete wavelet design for cardiac signal processing

Cited by 32 publications

References 5 publications

Improved Denoising Method for Ultrasonic Echo with Mother Wavelet Optimization and Best-Basis Selection

Improved Denoising Method for Ultrasonic Echo with Mother Wavelet Optimization and Best-Basis Selection

Analog Wavelet Filters: The Need for Approximation

Orthogonal Matched Wavelets with Vanishing Moments: A Sparsity Design Approach

Contact Info

Product

Resources

About