Efficient coding scheme for image wavelet representation in lossy compression scheme is presented. Spatial-frequency hierarchical structure of quantized coefficient and their statistics is analyzed to reduce any redundancy. We applied context-based linear magnitude predictor to fit 1st order conditional probability model in arithmetic coding of significant coefficients to local data characteristics and eliminate spatial and inter-scale dependencies. Sign information is also encoded by inter and intra-band prediction and entropy coding of prediction errors. But main feature of our algorithm deals with encoding way of zerotree structures. Additional symbol of zerotree root is included into magnitude data stream. Moreover, four neighbor zerotree roots with significant parent node are included in extended high-order context model of zerotrees. This significant parent is signed as significant zerotree root and information about these roots distribution is coded separately. The efficiency of presented coding scheme was tested in dyadic wavelet decomposition scheme with two quantization procedures. Simple scalar uniform quantizer and more complex space-frequency quantizer with adaptive data thresholding were used. The final results seem to be promising and competitive across the most effective wavelet compression methods.