Image Reconstruction using wavelet transform with extended fractional fourier Transform

Abstract: Image reconstruction forms the basis of many applications in the fields of medicine, astronomy etc. Historically an image is reconstructed using several methods of which Fourier and wavelet transform methods formed the roots of present day technologies. The reconstructed images possess higher resolution and helps in analyzing the image in more detail. In our thesis we proposed a method where we used fractional Fourier transform in conjunction with wavelet transform to produce the reconstructed image. We employed three wavelets in our thesis namely Haar wavelet, Daubechies wavelet and Coiflet wavelet in order to gain diversity into our results. For the scaling function of each of the three wavelets fractional Fourier transform is applied which gives a new scaling function. A new wavelet function created using the scaling function. Such a wavelet is applied to series of images of various resolutions (256x256, 128x128, 64x64) and is encrypted using DES before transmitting over the channel. The reconstruction is carried out using inverse DES and inverse wavelet Transform to get the reconstructed image. The parameters we used to determine the efficiency of the wavelets are peak signal to noise ratio(PSNR) and Structural similarity Index(SSIM). The results for various images are plotted using box plots. We reached out the conclusions that Daubechies had the better performance compared to other wavelets. Also the performance falls down with the image resolution.