Image Compression Based On The Second Generation Bandelets And SPIHT

As one of the key technologies of image storage and transmission, image compression encoding has been the hotspot in image processing field. Wavelet transform, which can overcome the disadvantage of classical Fourier analysis, shows its good prospect as a multi-scale analysis tool in image compression. It not only has localized property, but also capable of processing the non-stationary signals and adapting to human visual characteristics. Bandelets transform, which can obtain sparse image representation by tracking the image geometric directions adaptively, is a multi-scale geometric analysis tool. It can realize the optimal approximation of two-dimensional function with C q singular curves. So it has great advantage and potential in image compression. Focusing on Wavelet and Bandelets transform, the paper has done the following works:(1)In this paper, we proposed a Set Partitioning in Hierarchical Trees (SPIHT) encoding method based on K-means Clustering. SPIHT algorithm is based on the idea of embedded zero-tree coding algorithm which mainly uses the correlation among different directional sub-bands, but does not fully take into account the correlation among adjacent elements in the same sub-band. For the above shortcomings, this paper firstly organizes the wavelet coefficients with the same properties in the wavelet low-frequency sub-band, and then pre-process coefficients to reduce the encoding bits of wavelet coefficients. This method overcomes the shortcomings of the embedded zero tree wavelet coding algorithm, reduces the number of coding bits fully with redundancy within the sub-band and achieves the purpose of image compression.(2)In this paper, we proposed SPHIT coding method based on fixed partition 2G Bandelets. This method adapts fixed partition idea in order to avoid the quadtree combination course from bottom to up, which can greatly reduce the complexity in time and space. At the same time, SPHIT coding based on fixed partition 2G Bandelets is proposed by an investigation of the relationship of distribution features between Bandelets coefficient and wavelet coefficient. This proposed algorithm can availably reduce the complexity of the compression algorithm and improve the coding efficiency to a certain extend.(3)In this paper, we proposed a cost function which matches Embedded Block Coding with Optimal Truncation (EBCOT) based 2G Bandelets transform. Although the SPIHT coding algorithm based on fixed partition 2G Bandelets can improve the coding efficiency to a certain extend, the searching of the optimized geometric flow is controlled by the quantization threshold T. Different quantization thresholds are corresponding to different geometric flows, and the Bandelets coefficients attained are different. So, after coding the Bandelets coefficients using SPIHT, the results are different too. Based on it, a new cost function which matches the coding strategy is proposed in this paper. It is not related with the quantization threshold T, and can reduce the complexity and improves the stability of the proposed algorithm. Additionally, by combining the EBCOT coding method used in JPEG 2000, we can improve the coding efficiency further.This paper is supported by the National Nature Science Foundation of China (Nos.60601029, 60971112).