  We present a numerical method for calculating piecewise smooth spectral
functions of correlated quantum systems in the thermodynamic limit from the
spectra of finite systems computed using the dynamical or correction-vector
density-matrix renormalization group method. The key idea is to consider this
problem as a blind deconvolution with an unknown kernel which causes both a
broadening and finite-size corrections of the spectrum. In practice, the method
reduces to a least-square optimization under non-linear constraints which
enforce the positivity and piecewise smoothness of spectral functions. The
method is demonstrated on the single-particle density of states of
one-dimensional paramagnetic Mott insulators represented by the half-filled
Hubbard model on an open chain. Our results confirm that the density of states
has a step-like shape but no square-root singularity at the spectrum onset.
