  Motivated by a recent work on a preconditioned MINRES for flipped linear
systems in imaging, in this note we extend the scope of that research for
including more precise boundary conditions such as reflective and
anti-reflective ones. We prove spectral results for the matrix-sequences
associated to the original problem, which justify the use of the MINRES in the
current setting. The theoretical spectral analysis is supported by a wide
variety of numerical experiments, concerning the visualization of the spectra
of the original matrices in various ways. We also report numerical tests
regarding the convergence speed and regularization features of the associated
GMRES and MINRES methods. Conclusions and open problems end the present study.
