From the course: Wavelet Analysis: Concepts with Wolfram Language

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Wavelet best basis

Wavelet best basis - Wolfram Language Tutorial

From the course: Wavelet Analysis: Concepts with Wolfram Language

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Wavelet best basis

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So now that we have talked about the wavelet basis, we have talked about the coarse and the detail coefficients, let us now delve into the idea of what are called as Wavelet Best Basis. Wavelet best basis is essentially an optimal representation of the data in the wavelet domain, such that it minimizes a certain cost function. The applications where wavelet best basis become very prominent is in the field of denoising or data compression, or a certain image analysis. So in order to better understand wavelet best basis, let's make use of a simple example. In this case, I'm going to make use of the following example. And the idea is to perform a wavelet decomposition on this and then figure out what the wavelet best bases are. If I were to perform just a discrete wavelet transform and also a discrete wavelet packet transform and plot the tree view of that, you will notice that for a wavelet packet transform, the coarse and the detail coefficients have to be decomposed. On the other…

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