Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Computer Vision and Pattern Recognition Unit (CVPR-Kolkata)


Purui, Swapan Kumar (CVPR-Kolkata; ISI)

Abstract (Summary of the Work)

In this thesis, we propose two new subband transforms entitled ISITRA and YKSK transforms and their possible applications in image compression and encryption. Both these transforms are developed based on a common model of multiplication known as Bino’s model of multiplication. ISITRA is a convolution based transforms i.e., that both forward and inverse transform of ISITRA is based on convolution as in DWT or 2-channel filter bank. However, it is much more general than the existing DWT or 2-channel filter bank scheme in the sense that it we can get different kinds of filters in addition to the filters specified for perfect reconstruction in the existing 2-channel filter bank. ISITRA eliminates the difficulty of finding perfect reconstruction filters in 2-channel subband scheme and provides the ways of finding better filter coefficients for different purposes. Also, we can generate different forms of decomposition and reconstruction in ISITRA. Multi-resolution signal decomposition is also possible in ISITRA using multilevel decomposition scheme. Moreover, we can also get perfect reconstruction multi-channel filter bank and multichannel transmultiplexer. YKSK transform is also a generalized subband transform like ISITRA. Its forward transform is based on convolution but its inverse transform is based on deconvolution and hence filters can be chosen arbitrarily. YKSK transform has three main types, namely, fixed length type, semi-infinite length type and infinite length type. Multi-stage decomposition is possible in YKSK transform. Integer version of the YKSK transform can easily be obtained. Both multilevel half and multilevel full decomposition can also be performed in YKSK transform. Multilevel decomposition of fixed length type gives multi-resolution signal decomposition as in ISITRA. Multilevel decomposition in the case of infinite length case gives distorted signal components. Lastly, we use ISITRA for lossy image compression and YKSK transform for image encryption. Every lossy compression scheme requires good coding schemes besides the subband transform used. We propose two coding schemes ISPIHT and DPC for subband based lossy image compression scheme. ISPIHT is an improved SPIHT in terms of speed and memory requirement. However, its performance remains the same as that of SPIHT. DPC is a very simple and significantly faster new subband coding scheme with low memory requirement. The popular subband coders, EZW, SPIHT, EBCOT and JPEG2000 are yet to find a proper place in the hardware or chip world because of their complex algorithm and requirement of large memory space. DPC, however, it is marginally less in compression performance as compared to SPIHT and JPEG2000, has no such problems and hence would be of immense interest for hardware designers. We also suggest some PRF sets of length-10 having the same frameworks as that of 9/7 filters, which perform better in some images. For the use of YKSK transform for encryption, we develop meitei lock sequence to provide tight security for our encryption scheme. Meitei lock sequence is a good random number sequence generator and may become an essential part of every secure encryption scheme in future.


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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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Mathematics Commons