## Image reconstruction using symmetric convolution and discrete trigonometric transforms

JOSA A, Vol. 15, Issue 11, pp. 2827-2840 (1998)

http://dx.doi.org/10.1364/JOSAA.15.002827

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### Abstract

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.

© 1998 Optical Society of America

**OCIS Codes**

(100.0100) Image processing : Image processing

(100.1830) Image processing : Deconvolution

(100.2000) Image processing : Digital image processing

(100.2960) Image processing : Image analysis

(100.2980) Image processing : Image enhancement

(100.3020) Image processing : Image reconstruction-restoration

**Citation**

T. M. Foltz and B. M. Welsh, "Image reconstruction using symmetric convolution and discrete trigonometric transforms," J. Opt. Soc. Am. A **15**, 2827-2840 (1998)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-11-2827

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