Modern Spectrum Analysis in NMR

When N = M, Parseval’s Theorem
MaxEnt: analytic solution
Donoho, Johnstone, Stern, and Hoch PNAS 87, 5066-5068 (1990)
in essence allowing us to compute C(d) in the frequency domain, and
finding the critical point of the objective function Q = S - λC is easy.
The MaxEnt reconstruction ( ˆ f ) then reduces to applying the
transformation
that is the solution to
to the f (the DFT of d)
! " z
0 = ! log" +1 ! 2# " ! Re z
N
2
2
" d ˆ i ! d i = " f ˆ j ! f j
i
M
j