A log spectral approach to bidirectional deconvolution

ALGORITHM

Here we fill in more details of the algorithm. After we are certain of its behavior we would naturally switch over to conjugate directions.

D(omega,x) = FT d(t,x)
u=0;
iteration {
        U = FT(u)
        remove mean from U(omega)
        exp(U(Z))
        dU = 0
        for all x
                r(t,x) = IFT( D exp(U) )
                softclip( r )
                dU += conjg(FT(r)) * FT(softclip)        #  "*" means multiply
        remove mean from dU(omega)
        for all x
                dR = FT(r) * dU                          #  "*" means multiply
                dr = IFT(dR)
        argmin(alpha) = H(r+alpha*dr)
        u = u + alpha du 
        }