Dual Tree Wavelet Transforms in Image Compression

The theory and applications of wavelets have undoubtedly dominated the journals in all mathematical, engineering and related fields throughout the last decade. A variety of powerful and sophisticated wavelet-based schemes for image compression have been developed and implemented. Nevertheless these traditional approaches secure some severe limitations. Wavelets for example fail to capture regularities of contours, since they are not able to sparsely represent one dimensional singularity of 2-D signals. Recent developments in Complex Wavelet Transforms are classified into two important classes, Redundant CWT (RCWT), and Non-Redundant CWT (NRCWT). The important forms of RCWT include Kingsbury’s and Seles nick’s Dual-Tree DWT (DT-DWT), that actually is taken for comparison in the paper. These redundant transforms consist of two conventional DWT filter bank trees working in parallel with respective filters of both the trees in approximate quadrature to obtain real and imaginary part of complex wavelet coefficients. This introduces limited redundancy and allows the transform to provide approximate shift variance and directionally selective filters while preserving the usual properties of perfect reconstruction and computational efficiency with good well balanced frequency responses. Set Partitioning In Hierarchical Trees algorithm (SPIHT) is used to compress images. Experimental results show that DT-DWT (K) coder outperforms DT-DWT(S) at all bit rates.