Could you tell me why wavelets without scaling functions can't be used for two-dimensional analysis? What is the role of scaling function?
,,A wavelet'' actually is two functions that are orthogonal to each other. That way, a signal can be split into two parts. One part is the wavelet proper, while the other is usually called ,,scaling function'' (sometimes ,,mother wavelet'' as well). When you have just one of both, you can not perform a meaningful wavelet transform.