Resolution-to-noise trade-off in linear image restoration

The incorporation of both spatial and spectral adaptivity in a linear restoration algorithm is addressed. The formulation of a combined criterion is proposed, involving the minimum-mean-square-error (MMSE) and the least-mean-square-error (LMSE) criteria, in portions controlled by an indicator of the spatial signal activity. The incorporation of spectral adaptivity is achieved through the use of a decorrelating matrix in each individual criterion. The restoration algorithm derived, called the resolution-to-noise trade-off (RNT) algorithm, offers the flexibility of applying either linear MMSE (Wiener) filtering, inverse filtering, or no filtering at all, depending on the indicator of the spatial signal activity and the decorrelating matrices. The relationship of the RNT algorithm to other linear noniterative restoration approaches is discussed. it is indicated that the RNT filter forms a generalization of restoration filters that involve the point-spread function (psf) in a linear fashion