Designing a separate filter for each patch

Recall the 2-D prediction-error filter subroutine pef2() . Given a data plane, this subroutine finds a filter that tends to whiten the spectrum of that data plane. The output is white residual. Now suppose we have a data plane where the dip spectrum is changing from place to place. Here it is natural to apply subroutine pef2() in local patches. This is done by subroutine lopef2(). First it builds the tent weights and erases the output residual. Then it loops over all patches. Then it calls pef2() to get the prediction residual for the patch. Next, to weight the residual by the window weight diag() is used, and the patches are reassembled. Finally the wall weight multiplies the reassembly, so that patch overlap is accounted for.  

# lopef2  -- LOcal Prediction Error Filter in 2-D
#
subroutine lopef2( data, resi, n1,n2,w1,w2,k1,k2, niter, lag1,lag2, afre, a1,a2)
integer     i1,i2, n1,n2,w1,w2,k1,k2, niter, lag1,lag2,                   a1,a2
real              data(n1,n2),resi(n1,n2),                           afre(a1,a2)
temporary real  wallwt(n1,n2),                                       aa(  a1,a2)
temporary real  pdata(w1,w2), presi(w1,w2),  windwt(w1,w2)
call     tent2(                         a1,a2, lag1,lag2, windwt,w1,w2)
call null(                                                resi,  n1*n2)
do i2= 1, k2 {
do i1= 1, k1 {
        call patch2( 0,0, i1,i2,k1,k2, data,n1,n2,pdata, w1,w2)
        call pef2( pdata,presi, w1,w2, niter,lag1,lag2,afre,aa,a1,a2)
        call diag( 0, 0, windwt, w1*w2,     presi,presi        )
        call patch2( 1,1, i1,i2,k1,k2, resi,n1,n2,presi, w1,w2)
        }}
call mkwallwt2( k1,k2, windwt, w1,w2, wallwt, n1,n2)
call diag  (       0, 0,              wallwt, n1*n2,   resi, resi )
return; end

The output of lopef2() is necessarily zero around some of its outer periphery because that of pef2() is so. The output borders necessarily have some zeros because filter outputs are smaller than the inputs. Where this happens, I usually replace the (zero) output by the input (scaled by the variance ratio).