A local spatial convolution filter is suggested whose design is based on approximating a global optimal restoration filter, the Parametric Projection Filter (PPF). The PPF tries to construct a restored signal or image that is optimally close to each individual original signal, with the noise level as low as possible. The local filter provides a restoration that is as close as possible to the PPF restoration. The design is accomplished by least squares techique in Fourier domain. Once the PPF is available, the main task is to solve a set of linear normal equations whose coefficient size depends on the size of the local filter. It is shown by examples using both one- and two-dimensional signals that the restorations are satisfactory even when the filter size is considerably smaller than the width of the degradation.
[1]
B E Saleh.
Trade off between resolution and noise in restoration by superposition of images.
,
1974,
Applied optics.
[2]
Martin J. Lahart.
Local image restoration by a least-squares method
,
1979
.
[3]
C. K. Yuen,et al.
Theory and Application of Digital Signal Processing
,
1978,
IEEE Transactions on Systems, Man, and Cybernetics.
[4]
Erkki Oja,et al.
Parametric projection filter for image and signal restoration
,
1986,
IEEE Trans. Acoust. Speech Signal Process..
[5]
B. Roy Frieden.
Image restoration by discrete convolution of minimal length
,
1974
.