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This paper presents a listless variant of a modified three-dimensional (3D)-block coding algorithm suitable for medical image compression. A higher degree of correlation is achieved by using a 3D hybrid transform. The 3D hybrid transform is performed by a wavelet transform in the spatial dimension and a Karhunen–Loueve transform in the spectral dimension. The 3D transformed coefficients are arranged in a one-dimensional (1D) fashion, as in the hierarchical nature of the wavelet-coefficient distribution strategy. A novel listless block coding algorithm is applied to the mapped 1D coefficients which encode in an ordered-bit-plane fashion. The algorithm originates from the most significant bit plane and terminates at the least significant bit plane to generate an embedded bit stream, as in 3D-SPIHT. The proposed algorithm is called 3D hierarchical listless block (3D-HLCK), which exhibits better compression performance than that exhibited by 3D-SPIHT. Further, it is highly competitive with some of the state-of-the-art 3D wavelet coders for a wide range of bit rates for magnetic resonance, digital imaging and communication in medicine and angiogram images. 3D-HLCK provides rate and resolution scalability similar to those provided by 3D-SPIHT and 3D-SPECK. In addition, a significant memory reduction is achieved owing to the listless nature of 3D-HLCK.

Uncompressed image data requires considerable storage capacity and transmission bandwidth. Despite rapid progress in mass-storage density, processor speeds, and digital communication system performance, demand for data storage capacity and data transmission bandwidth continues to outstrip the capabilities of available technologies. Images require substantial storage and transmission resources, thus image compression is advantageous to reduce these requirements. Different wavelets will be used to carry out the transform of test image and the results will be analyzed in terms of Peak signal to noise ratio obtained and the computation time taken for decomposition and reconstruction. The orthogonal wavelet used are Daubechies family of Haar (Daubechies 1), Daubechies 2, Daubechies 3, Daubechies 4, Daubechies 5, and Coiflet families, as well as Symlet families.. The wavelet which has the highest PSNR in each family is Haar(db),Coiflet1,andSymlet 2 and less computation time in each family is Haar(db1), symlet3, 4, 6 and coiflet1.

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