  A new approach of solving the ill-conditioned inverse problem for analytical
continuation is proposed. The root of the problem lies in the fact that even
tiny noise of imaginary-time input data has a serious impact on the inferred
real-frequency spectra. By means of a modern regularization technique, we
eliminate redundant degrees of freedom that essentially carry the noise,
leaving only relevant information unaffected by the noise. The resultant
spectrum is represented with minimal bases and thus a stable analytical
continuation is achieved. This framework further provides a tool for analyzing
to what extent the Monte Carlo data need to be accurate to resolve details of
an expected spectral function.
