  We present a new form of the multi-boson reduction of KP hierarchy with Lax
operator written in terms of boson fields abelianizing the second Hamiltonian
structure. This extends the classical Miura transformation and the
Kupershmidt-Wilson theorem from the (m)KdV to the KP case. A remarkable
relationship is uncovered between the higher Hamiltonian structures and the
corresponding Miura transformations of KP hierarchy, on one hand, and the
discrete integrable models living on {\em refinements} of the original lattice
connected with the underlying multi-matrix models, on the other hand. For the
second KP Hamiltonian structure, worked out in details, this amounts to finding
a series of representations of the nonlinear $\hWinf$ algebra in terms of
arbitrary finite number of canonical pairs of free fields.
