Do a float wavelet transform with the lowest-entropy wavelet (D97,CDF22,Haar,whatever). The imagine is now an LL and a series of bands, HL1,HL2,...HH1,...
Fit the linear relationship of bands : HLn ~= C * HLn-1. Fit the best C for all n. Seperate constant for HH and LH.
Use this linear relationship to add new LH,HL,HH bands with the scaled data. Perhaps also apply an additional user-specified scale. Do the inverse transform. The resulting image is 2X bigger in each dimension.
This will do things like zoom hard diagonal lines perfectly due to the wavelet zoom scale invariance property.
ps. this doesn't actually work because Band (n) to (n-1) correlation is very strong for coefficient magnitude, but not for signs, which are hard to predict.