To increase the fields that can be covered with applying Wavelet transformations inside it, we need to know any related cases that need or can get benefits of applying the WT.
Good question my friend, however, we may have to specify which type of WT we need to investigate... the continuous wavelet transform and wavelet coherence is widely used in biomedical applications or in any application that require scrutinising a non stationary signal in the time-frequency domain ... finding high power region....and it does not require an inverse transform. Whereas the DWT is useful in different applications that require signal enhancement by analysing the signal, do some processing such as denoising etc, then an inverse DWT for perfect signal reconstruction.
The Discrete Wavelet Transform (DWT) approximation coefficient is a low-resolution version of the original image. Apart from noise reduction to some extent it will not provide any extra feature for classification. The detail coefficients on the other hand will provide information regarding texture orientations along specific directions, which can be used for classification, if certain classes are characterized by strong textures along specific directions.