A lossless image compression algorithm using wavelets and fractional Fourier transform

Abstract

The necessity of data transfer at a high speed, in fast-growing information technology, depends on compression algorithms. Maintaining quality of data reconstructed at high compression rate is a very difficult part of the data compression technique. In this paper, a new lossless image compression algorithm is proposed, which uses both wavelet and fractional transforms for image compression. Even though wavelets are the best choice for feature extraction from the source image at different frequency resolutions, the low-frequency sub-bands of wavelet decomposition are the untouched part in compression method in most of the existing methods. On the other hand, fractional Fourier transform is a convenient form of generalized Fourier transform that helps in the compact lossless coding of the source image with optimal fractional orders. Hence, we have used discrete fractional Fourier transform to compress those sensitive sub-bands of the wavelet transform, carefully. In this method, an image is split into low- and high-frequency sub-bands by using Daubechies wavelet filter and level 1 quantization is applied for both low-frequency and high-frequency sub-bands. The low-frequency sub-bands are compressed by using fractional Fourier transform with optimal fractional orders, and at the same time, high-frequency sub-bands are compressed by eliminating zeroes and storing only nonzero blocks and its position. The compressed wavelet coefficients are further compressed by the application of level 2 quantization and stored as a reduced array. This reduced array is encoded by using arithmetic encoder followed by run-length coding. The experimental results of the proposed algorithm with a different set of test images are compared with some of the existing image compression algorithms. The results show that the proposed method has significant improvement in image reconstruction quality.