To find how much the signal/Image may have been zoomed use the following iteration scheme to see the convergence of scale value(a).
Idea is to compute differential of u(at) wrto a ,Here t is the independent variable , a is the scaling factor. call it u*(a) for fixed t=t0
Now compute the sequence (a_n), for a_0=1
a_n+1=a_n+{u2(t0)-u1(t0*a_n)}/u_1*(a=a_n)
Another approach is variational approach:
da/dt=integral (abs(u2(t)-u1(at)) *u1(at)) wrto t over all the domain.
solve the above DE for stationary solution of a.
P.S: variational approach is expected to be more effective.
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