Image Compression and Reconstruction using Discrete Rajan Transform Based Spectral Sparsing

As a contribution from research conducted by many, various image compression techniques have been developed on the basis of transformation or decomposition algorithms. The compressibility of a signal is seen to be affected by the entropy in the signal. Compressibility is high if the energy distribution is concentrated in fewer coefficients. It is reasonable to expect that sparse signals have a highly compressible nature. Thus, sparse representations have potential uses in image compression techniques. There are many techniques used for this purpose. As an alternative to these traditional approaches, the use of Discrete Rajan Transform for sparsification and image compression was explored in this paper. The simulation results show that higher quality compression can be achieved for images using Discrete Rajan Transform in comparison with other popular transforms like Discrete Cosine Transform, and Discrete Wavelet Transform. The results of the experiment were analyzed on the basis of seven quality measurement parameters – Mean Squared Error, Peak Signal to Noise ratio, Normalized Cross-Correlation, Average Difference, Structural Content, Maximum Difference, and Normalized Absolute Error. It was observed that Discrete Rajan Transform is effective in introducing sparsity in images and thereby improving compressibility.