in equation 3 can be recovered iteratively using shaping regularization:
shapes the estimated model into the space of admissible models at each iteration (Fomel, 2008,2007) and
is the backward operator that provides an inverse mapping from data space to model space.
Daubechies et al. (2004) prove that, if
is a nonlinear thresholding operator (Donoho and Johnstone, 1994),
is the adjoint operator of
, iteration 5 converges to the solution of equation 6 with
is the threshold and
denotes a sparsity-promoting transform.
A better choice for
is the pseudoinverse of
(Daubechies et al., 2008).
Iterative deblending of simultaneous-source seismic data using seislet-domain shaping regularization