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Image and video processing using discrete fractional transforms

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Abstract

The mathematical transforms such as Fourier transform, wavelet transform and fractional Fourier transform have long been influential mathematical tools in information processing. These transforms process signal from time to frequency domain or in joint time–frequency domain. In this paper, with the aim to review a concise and self-reliant course, the discrete fractional transforms have been comprehensively and systematically treated from the signal processing point of view. Beginning from the definitions of fractional transforms, discrete fractional Fourier transforms, discrete fractional Cosine transforms and discrete fractional Hartley transforms, the paper discusses their applications in image and video compression and encryption. The significant features of discrete fractional transforms benefit from their extra degree of freedom that is provided by fractional orders. Comparison of performance states that discrete fractional Fourier transform is superior in compression, while discrete fractional cosine transform is better in encryption of image and video. Mean square error and peak signal-to-noise ratio with optimum fractional order are considered quality check parameters in image and video.

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Acknowledgments

The authors acknowledge the support provided by the Department of Electronics & Communication Engineering, Thapar University Patiala, Punjab (India), for carrying out the Research work and anonymous reviewers for their valuable suggestions.

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Correspondence to Neeru Jindal.

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Jindal, N., Singh, K. Image and video processing using discrete fractional transforms. SIViP 8, 1543–1553 (2014). https://doi.org/10.1007/s11760-012-0391-4

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