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. The block based fractional transforms are used due to its energy compacting property and relative easy implementation. However, annoying blocking artifacts are noted at high compression percentages as each block is transformed and quantized independently. These artifacts degrade the reconstructed image quality. These artifacts have been analysed for fractional Fourier transform and fractional Cosine transforms and has given more affect in fractional Cosine transforms. The compressed images also need security while being transferred. There are many algorithms available in literature to provide security to compressed images. So, an algorithm to obtain the security of compressed images using scrambling is suggested in this work. It has been established that the improved scrambling degree from existing method is attained. The fractional keys used for compression also provide the security to compressed image. Next to compression, the fractional Fourier transforms and fractional Cosine transforms are also used in image encryption algorithms. It is shown that peak signal to noise ratio of fractional Cosine transforms is superior to fractional Fourier transforms in image encryption. The variation of fractional keys has been done in this work and it is observed that security is enhanced. The images have been encrypted using two, three and four fractional keys and taken the advantage of extra keys of fractional transforms. The sensitivity of fractional keys in decryption is also shown and observed that for proper decryption all the fractional keys and random phase masks should be correct. The popularity of digital library applications and internet commerce has increased the demand of security in the mind of content providers. The algorithm for image encryption and scrambling is suggested in this work. In scrambling, the positions of pixels are shuffled and the scrambled image becomes unrecognizable. So, scrambling enhance the security as the invader has to crack the fractional keys as well as descrambling algorithm. A joint algorithm is suggested based on the preceding observations. The images are compressed using fractional Fourier transforms and encrypted using fractional Cosine transforms. There are two approaches for joint algorithm compression-encryption and encryption-compression. It is established by comparing these two techniques that the former is better, because the data to be encrypted is compressed earlier. The work has been extended from still images to video. The video is motion of images including the time parameter. The video signal is encrypted using fractional transforms. The noise effects have been also analyzed in video encryption. Video is also compressed-encrypted using fractional transforms. Frames are extracted from video. The difference frame is compressed and encrypted. At various compression percentages, the proposed algorithm is observed better from SCAN method based on quality parameters. Finally, the proposed image and video processing techniques has proven the efficacy of fractional transforms and motivated to develop more application in future.