Finite Field Discrete Cosine Transform for Image Processing Applications
Salila Hegde1, Rohini Nagapadma2
1Salila Hegde, Department of ECE, NIE Institute of Technology, Mysore (Karnataka), India.
2Rohini Nagapadma, Department of ECE, National Institute of Engineering, Mysore (Karnataka), India.
Manuscript received on 18 June 2019 | Revised Manuscript received on 25 June 2019 | Manuscript published on 30 June 2019 | PP: 2529-2533 | Volume-8 Issue-5, June 2019 | Retrieval Number: E7748068519/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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 8×8 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.
Keywords: DCT, Error Detection, FFCT, Finite Field, Image Compression.
Scope of the Article: Image Processing