  The spectral functions and corresponding self energies are calculated within
the planar t-t'-J model as relevant to hole-doped cuprates using the exact
diagonalization method at finite temperatures, combined with the averaging over
twisted boundary conditions. Results show truncated Fermi surface at low doping
and t'<0 in the antinodal region while the self energy reveals weakly k- and
doping dependent anomalous relaxation rate |\Sigma''(k,\omega)|~ a+b|\omega|
for \omega<0, consistent with recent ARPES results, and a pseudogap-generating
component of Lorentzian form. The latter is well pronounced at low doping and
strongly depends on k and t'.
