Image reconstruction using symmetric convolution and discrete trigonometric transforms

We demonstrate how the symmetric convolution-multiplication property of the discrete trigonometric transforms can be applied to problems in image reconstruction. This property allows for linear filtering of degraded images by means of point-by-point multiplication in the transform domain of trigonometric transforms. Specifically, in the transform domain of a type II discrete cosine transform, there is an asymptotically optimum energy compaction near d.c. for highly correlated images, which has advantages in reconstructing images with high-frequency noise. The symmetric convolution-multiplication property allows for scalar representations in the transform-domain space of discrete trigonometric transforms for linear reconstruction filters such as the Wiener filter. An analysis of the scalar Wiener filter's performance in the trigonometric transform domain is given. (C) 1998 Optical Society of America. [S0740-3232(98)00511-0]. OCIS codes: 100.0100, 100.1830, 100.2000, 100.2960, 100.2980, 100.3020.