On the treatment of boundary artifacts in image restoration by reflection and/or anti-reflection

The abrupt boundary truncation of an image introduces artifacts in the restored image. For large image restoration with shift- invariant blurring, it is advisable to use Fast Fourier Transform (FFT)- based procedures for reducing the computational effort. In this direction several techniques manipulate the observed image at the boundary or make some assumptions on the boundary of the true image, in such a way that FFT-based algorithms can be used. We compare the use of reflection with that of anti-reflection, in connection with the choice of the boundary conditions or for extending the observed image, both theoretically and numerically. Furthermore, we combine the two proposals. More precisely we apply anti-reflection, followed by reflection if necessary, to the observed image and we observe that the resulting restoration quality is increased with respect to the case ofplain reflection.