Wavelet tree structure-based image compression
Wu, Jincheng, writer on electrical engineering
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This paper presents an algorithm for image compression which involves tree structure coding (TSC) of wavelet coefficients resulting from discrete wavelet transform (DWT), successive approximation quantization, and entropy coding of symbols generated in tree structure encoder. The properties of the discrete wavelet transform were studied and it has been shown that any signal can be decomposed on a wavelet orthogonal basis. The decomposition defines pyramid multiresolution representation called wavelet representation. For images, this wavelet representation differentiates three spatial orientations. The TSC scheme exploits the self-similarity inherent in the wavelet representation to predict the properties of wavelet coefficients across different resolutions in each orientation. It has been shown that in the wavelet representation, every coefficient at a given resolution, with the exception of those in the highest resolution, can be related to a set of coefficients of the same orientation at the next finer resolution. This relationship is exploited by representing these coefficients as a data structure called a wavelet tree. The wavelet trees are quantized by using the simplest and more precise quantization, called successive approximation quantization, and then encoded as one of six tree symbols which are defined with the properties of the wavelet trees. The symbols are entropy coded via Huffman coding, which provides fast and efficient coding of the streams of the symbols. The TSC scheme has several prominent features that enable it to perform well on very low bit rate image compression. The performance of the scheme was evaluated through several quantitative measures, namely mean square error, peak signal to noise ratio, compression rate, etc. Excellent reconstructed images were obtained and demonstrate that the performance of the new image coding scheme is very competitive with all known wavelet-based compression algorithms.