Performance of fractional transforms in image and video processing

Abstract

Fourier transform is an important mathematical tool which is used in signal processing. The generalization of Fourier transforms are fractional Fourier transforms. Similarly, the other transforms available in mathematics can be fractionalized. The additional degree of freedom provided by fractional orders of fractional transforms has encouraged the researchers for its use in many applications. The fractional transforms are used in many applications of optics and signal processing area. The aim of this work is to explore the utilization of fractional transforms in image and video applications. The main bottleneck of image and video signals is privacy and saving of memory space in internet applications. Compression and encryption are the solutions for efficient transmission of image and video signals. So, the main contribution of research done in thesis is to develop better compression and encryption algorithms for image and video signals. The images have been compressed using fractional Fourier transforms, fractional Cosine transforms and fractional Hartley transforms. When image is compressed in the transform domain, they are generally divided into sub blocks. So, the block size is varied for these fractional transforms by dividing the image into N × N blocks, where N is 4, 8, 16 and 32. It has been observed that 8 × 8 block size for fractional Fourier transforms, 32 × 32 block size for fractional Cosine transforms and 4×4 block size for fractional Hartley transforms is better by simulation approach. The comparison of these transforms has determined the superiority of fractional Fourier transforms in image compression applications. Then image compression at various compression percentages is performed. The peak signal to noise ratio and mean square error are taken as quality parameters of reconstructed images. Also, the fractional Fourier transforms and fractional Cosine transforms are compared with existing Joint Photographic Expert Group method and observed as better.