What are the "wavelet planes" in a Stationary Wavelet Transform?

Question

Several articles, like Detection of superimposed periodic signals using wavelets and À Trous Wavelet Decomposition Applied to Image Edge Detection mention "wavelet planes" but I do not understand what these are.

In wikipedia and in a python package to calculate wavelet decomposition, there is no reference to "wavelet planes". Are these the list of approximation and details coefficients (such as the output of the function on the package)?

Answer 1

Explains it in the article it's been linked:

The algorithm can decompose an image (or a signal) into an approximate signal and a detail signal at a scale, the detail signal is called a wavelet plane, which is same as the original image in dimension.

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Basically Wavelet is an algorithmic technique (similar to trees not exactly though) that decomposes 1-D or 2-D time-series data, mapping them into low-frequency and high-frequency data using convolution theories.

• Those high frequency data is called Details or here "wavelet plane" (never actually heard this term before).

• The low-frequency data is generally referred to as Approximations.

• The above decomposition is one of the existing one.

Example of mapping in an image:

Another Example

• Ref 1

• Ref 2