Joël Karel - Wavelet Design

Matched scalar wavelet design

The design of scalar wavelets for matching it to prototype signals.

Orthogonal scalar wavelet design

We design orthogonal wavelets such that they have a sparse representation in the wavelet domain for a prototype signal.

Publications:

Orthogonal matched wavelets with vanishing moments: a sparsity design approach - Circuits, systems, and signal processing 2018
Data driven design of an orthogonal wavelet with vanishing moments - MTNS 2013
Optimal discrete wavelet design for cardiac signal processing - EMBC 2005

Software:

We have released the software covering the examples in the Circuits, systems, and signal processing 2018 paper, and this software is available for download on Zenodo. You can find a complete MATLAB implementation there.

Multiwavelet design

The design of multiwavelets for added flexibility compared to scalar wavelets. In principle this would function for multivariate signals, but one also can split univariate timeseries in multiple phases.

Multiwavelet design with balanced vanishing moments

We design multiwavelets such that they have a sparse representation in the wavelet domain for a prototype signal. In the case that the prototype signal is a univariate signal, it is important to have balanced vanishing moments. These are enforced by the parameterization.

Publications:

The design of matched balanced orthogonal multiwavelets - Frontiers in Applied Mathematics and Statistics 2022
Multiwavelet Design for Cardiac Signal Processing - EMBC 2006

Wavelet approximation

The approximation of wavelet function for implementenation in analog circuits.

Wavelet approximation for implementation in the analog domain

As part of the BioSens project we approximated wavelets by continuous-time linear systems, for implementation in analog circuits to ensure ultra-low power.

Publications:

Implementing Wavelets in Continuous Time Analog Circuits with Dynamic Range Optimization - IEEE Transactions on Circuits and Systems I, 2011
Wavelet approximation for implementation in dynamic translinear circuits - IFAC Proceedings Volumes, 2005
Analog complex wavelet filters - IEEE International Symposium on Circuits and Systems, 2005
An L2-based approach for wavelet approximation - Proceedings of the 44th IEEE Conference on Decision and Control, 2005
Ultra low-power analog Morlet wavelet filter in 0.18/spl mu/m BiCMOS technology - Proceedings of the 44th IEEE Conference on Decision and Control, 2005
Complex wavelet transform for analog signal processing - proc. ProRISC 2004

Wavelet applications

Various applications of wavelet theory.

Biomedical applications of wavelets

Publications:

Wavelet-promoted sparsity for non-invasive reconstruction of electrical activity of the heart - Medical & biological engineering & computing, 2018
Wavelet-sparsity based regularization over time in the inverse problem of electrocardiography - 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2010
Denoising of cardiac signals with optimal wavelets - Wave2006
QT interval measurement in cardiac signal processing with multiwavelets - First Dutch Conference on Bio-Medical Engineering, 2007