Finite field discrete cosine transform for image processing applications

Abstract

Discrete transforms such as DCT are found useful in several image processing applications. There exist discrete transforms for finite fields which use integer arithmetic. Discrete cosine transform over finite field (FFCT) is one such transform which uses k-cosine trigonometry. As all the arithmetic is carried out on integers the image processing algorithms based on FFCT do not suffer from round off errors as in DCT based algorithms. In this paper we investigate properties of FFCT and discuss parameters used for two dimensional FFCT pair. The transformation kernel over GF (p) where p is prime is calculated and FFCT of 8x8 regular test images are obtained. From the study of FFCT of the test images we suggest the application of this transform to detect one bit error that occurs in photo mask image of integrated circuits. An image compression algorithm is also implemented to show that FFCT based compression algorithms are lossless and yield higher compression ratio.