Satellite Image Processing Using Discrete Fractional Transforms

Abstract

With the development of space technology, the huge amount of data generated by new generation satellites to be used for a variety of upcoming applications. In order to save storage space and channel bandwidth, remote sensing image must be compressed before transmitted from a spacecraft. To increase productivity, reduce cost, facilitate innovation and virtual collaborative environment for addressing new challenges there exist inherent security risk of unauthorized access. To fulfill such security and privacy needs in various applications encryption of data is required. A lot of techniques are available for the above discussed applications and the hunger for improvement is underway. The fractional Fourier transform (FrFT) a generalization of Fourier transform (FT), introduced by Victor Namias in 1980 is an upcoming tool for the above applications because of an extra degree of freedom available to solve a problem [58]. With the advent of computers and enhanced computational capabilities the Discrete Fourier Transform (DFT) came into existence in evaluation of FT for real time processing. On similar lines, so there arises a need for discretization of FrFT. The Fractional transforms are almost in their infancy still having proved their worth to the optical and signal community by solving a variety of problems like, wave equation, Green’s function associated with quantum mechanical harmonic oscillator, propagation in graded index medium, which remained unsolved by previous generation transforms [41]. Further the compression of satellite image data can be optimized using some feature which can be extracted by Fractional transforms by using fractional convolution and correlation which has been discussed by various authors [7], [24], [41]. The extra degree of freedom available with fractional transforms which gives an extra key for encryption and improved compression makes it an active research topic for satellite images. With variation of its parameter ‘a’, it is found that by using fractional transforms, high visual quality decompressed image can be achieved for same amount of compression. By varying ‘a’ to different values, an optimum value of ‘a’ can be achieved with low mean square error (MSE), better peak signal to noise ratio (PSNR) i.e. better quality of decompressed image. The two fractional transforms like DFrFT and DFrCT are used for the compression of satellite images. The performance of these transforms is compared based iv on above said parameters i.e. MSE and PSNR. It has been observed that the performance of DFrFT is better than that of DFrCT. Moreover, the satellite images can be encrypted using fractional transforms which gives extra key for encryption provided by its fractional order. The performance of fractional transforms for satellite image encryption is compared based on PSNR and MSE. It has been observed that the value of PSNR is smaller for the case of DFrCT than that of DFrFT which proves the performance of DFrFT is better than DFrCT.