1) I am not sure about what you mean by "why", but generally we perform a wavelet transform of an image to get its wavelet coefficient or, if desired, its multi-resolution decomposition. The WT will allow to separate the image detais and approximation. The details are related to the high-frequency local components, like the edges, and the approximation is related to the total average.

2) It depends on what type of border treatment you use. If the image is MxN you will get an MxN decomposition if you use circular periodization, but other treatments give different sizes.

3) If you have Matlab with wavelet toolbox try "wavefun". If not, download and see documentation of Wavelab 8.50.

Regards.

Hi,

your questions are answered in the very good introduction into wavelets by Eric J. Stollnitz, Tony D. DeRose, and David H. Salesin. You can find it online at

http://grail.cs.washington.edu/projects/wavelets/article/