Space-variant generalised Gaussian regularisation for image restoration

Abstract

We propose a new space-variant regularisation term for variational image restoration based on the assumption that the gradient magnitudes of the target image distribute locally according to a half-Generalised Gaussian distribution. This leads to a highly flexible regulariser characterised by two per-pixel free parameters, which are automatically estimated from the observed image. The proposed regulariser is coupled with either the $L_2$ or the $L_1$ fidelity terms, in order to effectively deal with additive white Gaussian noise or impulsive noises such as, e.g. additive white Laplace and salt and pepper noise. The restored image is efficiently computed by means of an iterative numerical algorithm based on the alternating direction method of multipliers. Numerical examples indicate that the proposed regulariser holds the potential for achieving high-quality restorations for a wide range of target images characterised by different gradient distributions and for the different types of noise considered.

Keywords:

• Image restoration
• variational methods
• alternating direction method of multipliers
• half-Generalised Gaussian distribution

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research was supported by the ?National Group for Scientific Computation (GNCS-INDAM)? and by ex60 project by the University of Bologna ?Funds for selected research topics?.