Inquiry: Wavelet factorisation / Daubechies method /

In summary, if you are looking for resources on the factorisation technique for constructing non-standard wavelet filters, some helpful sources include the books "Wavelets: A Tutorial in Theory and Applications" by Charles K. Chui and "Wavelet Methods for Time Series Analysis" by Donald B. Percival and Andrew T. Walden, as well as online tutorials and reaching out to experts in the field for guidance.
  • #1
MednataMiza
43
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I need to construct a non-standard wavelet filter using the factorisation technique / Daubechies method / applied to the wavelet family / any /. I need to obtain the wavelet coefficients.
The problem is I can't even find a tutorial on how to perform the factorisation method.
I've read Ingird Daubechies Paper on factoring wavelet transforms into lifting steps, read everything Paul Abbott and Mark Maslen wrote and still can't even figure out if I am on the right track.
Everything is welcome: tutorials, guides, examples :)

Thanks !
 
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  • #3


Hi there,

I understand your frustration with trying to find resources on the factorisation technique for constructing non-standard wavelet filters. It can definitely be a complex and overwhelming topic to tackle on your own.

One resource that may be helpful is the book "Wavelets: A Tutorial in Theory and Applications" by Charles K. Chui. It covers the factorisation method in detail and provides step-by-step examples to help you understand the process.

Another helpful resource is the book "Wavelet Methods for Time Series Analysis" by Donald B. Percival and Andrew T. Walden. It also covers the factorisation method and provides practical examples and applications.

You may also want to check out online tutorials and lectures on the topic, such as those on the website of the International Society for Computational Biology (ISCB).

Lastly, don't be afraid to reach out to experts in the field for guidance. You can try contacting the authors of the papers you mentioned or reaching out to professors or researchers in the field for advice and resources.

I hope these suggestions help and good luck with your project!
 

1. What is inquiry in the context of wavelet factorisation?

Inquiry in the context of wavelet factorisation refers to the process of investigating and understanding the mathematical and computational principles behind the Daubechies method, which is a popular technique used for wavelet factorisation. It involves exploring the properties, advantages, and limitations of the method and its applications in signal and image processing.

2. How does the Daubechies method work in wavelet factorisation?

The Daubechies method is a multiresolution analysis technique that uses a set of wavelet functions, called Daubechies wavelets, to decompose a signal or image into different scales and frequencies. These wavelets are generated by scaling and shifting a mother wavelet, and they are able to capture both smooth and oscillatory features of the signal or image. The method involves a series of filtering and downsampling operations to obtain a compact representation of the signal or image.

3. What are the advantages of using the Daubechies method for wavelet factorisation?

The Daubechies method has several advantages, including its ability to provide a sparse representation of signals and images, which means it can efficiently remove noise and irrelevant information. It also allows for perfect reconstruction of the original signal or image, making it suitable for data compression. Additionally, the method has a fast and stable algorithm, making it computationally efficient.

4. What are the limitations of the Daubechies method in wavelet factorisation?

One limitation of the Daubechies method is its sensitivity to boundary effects, which can affect the accuracy of the wavelet coefficients at the edges of a signal or image. Another limitation is the selection of the appropriate wavelet order, which can impact the performance of the method. Additionally, the Daubechies wavelets are not orthogonal, which means they may not be suitable for certain applications that require orthogonal wavelets.

5. How is the Daubechies method used in practical applications?

The Daubechies method is widely used in various applications, including signal and image denoising, compression, and feature extraction. It has also been applied in fields such as data analysis, pattern recognition, and computer vision. The Daubechies wavelets have also been extended to 3D and higher-dimensional data, making the method applicable in areas such as medical imaging and geophysics.

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