Methods on how to reconstruct 1D signal from its approximation and detail coefficients at multilevel with Discrete Wavelet Transform (DWT)
The series of 1D multilevel discrete wavelet transform methods includes 3 parts:
Part I: Decomposition Method
Part II: Reconstruction Method
Part III: Partial Reconstruction Methods
In the last article, it demonstrates how to decompose a 1D signal into approximation and detail coefficients at multilevel levels. In this article, we will continue to see another part of the story of Wavelet transform, i.e. how to reconstruct signal from its approximation and detail coefficients.
Wavelet reconstruction transform, also known as wavelet synthesis, or inverse wavelet transform. If you are not familiar with the process of discrete wavelet reconstruction, you are recommended to read this article. It is also better to know about the methods of 1 stage (or single level) discrete wavelet reconstruction before moving on to learn the method to multilevels, because the single level reconstruction process is much easier to understand.