目的 针对现有小波域图像集合划分编码（SPC）方法存在无损编码性能较弱的问题，设计广义树分类器，构建嵌入广义树分类器的集合划分编码方法（SPACS_C）。方法 针对已有SPC方法对坐标集合直接进行"先检测后划分"编码，存在当位平面降低导致数据之间相关性降低后位置比特和不必要比特数量急剧增大问题，SPACS_C对编码过程中产生的坐标集合分类处理，减少对坐标集合的显著性检测次数，从而降低位置比特的输出。SPACS_C对广义树分类处理利用图像小波系数的稀疏度随位平面降低而迅速降低的数据特点，对"先划分后检测"和"先检测后划分"两种方式所需的比特开销进行预测，选用比特开销较少的方式编码坐标集合，减少SPACS_C输出的位置比特数量。结果 采用不同统计特性和不同大小的可见光图像（8 bit）和红外图像（16 bit）测试SPACS_C，结果表明SPACS_C的无损编码性能优于JPEG2000，特别是对红外图像的无损编码平均节省了3.1%的数据空间；性能接近或超过图像无损压缩标准JPEG-LS。结论 SPACS_C对坐标集合的分类处理利用小波域图像低层位平面稀疏度差的数据特点，有效减少位置比特输出，进而提高编码性能。与JPEG2000一样，SPACS_C可以实现图像质量的渐进式压缩。SPACS_C的编码不受图像数据动态范围的影响，可以对任意位深度的图像进行压缩编码。

Objective As a powerful image compression method, set partition coding (SPC) method effectively uses the correlation between the wavelet coefficients to obtain a higher data compression ratio, and it has been widely used for all types of image compression. The SPC method uses the idea of successive quantization approximation of the wavelet coefficient set, such as set partition coding system (SPACS), which partitions the coefficient set step-by-step to find significant coefficients and code them. A significance map was used to decide whether a set is significant, based on which set will be partitioned. If a set is significant, then SPC will output a location bit "1" and the set will be partitioned into 4 subsets; otherwise, the set is prepared for the next set coding operation. If set partition operations are conformable to the distribution of the insignificant coefficients, then location bits and unnecessary bits will be decreased. When the coefficient set is sparse, the SPC method can use fewer bits to encode the image. However, with the decrease of the bit plane, the sparseness of the coefficient set decreases, and the SPC method will waste many location and unnecessary bits, especially for lossless compression. To increase the lossless encoding performance of the set SPC method, we construct a set partition coding method that embeds a generalized tree classifier named SPACS_C. Method The previous SPC methods process all coordinate sets with "test before partition," thereby increasing the number of location and unnecessary bits when the correlation between data decreases. SPACS_C calculates the bit costs of two different coding ways called "test before partition" and "partition before test" for each coordinate set. Then, it chooses the one with lower bit cost to process the set. The process method used in SPACS_C takes advantage of the data characteristics in which the sparseness of bottom bit-planes decrease rapidly in wavelet transformed images. SPACS_C performs the coding process in the domain of the wavelet transform of the image. Daubechies (4, 4) integer wavelet transform is used in this study. The level of wavelet transform is determined by the image size. For instance, a level of 5 is recommended for an image with a spatial size of 512×512. Similar to SPACS, a general tree (GT) is used to simultaneously represent the tree and square sets in the wavelet domain. The processing flow of SPACS_C is as follows:1)Initialization. Let the threshold n be most significant digit of the maximum of the wavelet coefficient and the list of significant points (LSP) be an empty list. Add all GTs into the list of insignificant points (LIP), where all GTs that have descendants are added into the list of insignificant sets (LIS). 2)Sorting pass. Perform the significant test for every entry (i, j) in LIP. If the result is positive, bit=1, add GT (i, j; 1) into LSP to output the sign of the root node coefficient, and then remove (i, j) from LIP. For every entry in LIS, conduct prediction to calculate the bit costs of the two different coding ways called "test before partition" and "partition before test". The bit costs are the mathematical expectation of the bits used in coding using the two methods. If "test before partition" uses less bits than "partition before test", then do "test before partition". Otherwise do "partition before test". If the result of the "test before partition" is positive, then the out location bit "1" moves to the corresponding GT from LIP to LSP and outputs the sign of the root node coefficient. For "partition before test", the executed partition is removed from LIS. Let List1 be the partition result of a GT in LIS. Perform a significant test for every entry in List1. If the result is positive, partition the list to obtain a new set List2, and then place all entries at the end of LIS. Otherwise, place the entries at LIS. 3)Refinement pass. For every entry in LSP, if type=0, output the nth most significant bit, whereas if type=1, update type=0.4)Threshold update. Let n=n-1 and return to sorting pass until n is equal to 0 to achieve a lossless compression. In SPACS_C, the significant test is performed by a significant test function, where for any element c in a set C, if c ≥ 2ⁿ and c<2ⁿ⁺¹, then C is significantly relative to the threshold value 2ⁿ. Result Various visible and infrared images with different sizes, statistical properties, and bit depths were used to evaluate SPACS_C, and JPEG2000 and JPEG-LS were used for comparison. For SPACS_C, a 5-level Daubechies (4, 4) integer wavelet transform was used for decomposition. In addition, the wavelet coefficients were encoded. For infrared images with bit depths of 16 and 8 bits, the lossless encoding performance of SPACS_C was improved and became superior to that of JPEG2000; an average of 3.1% less bits were used by the former. Notably, JPEG-LS can only be used for 8-bit image compression. For visible images with 8-bit depth, SPACS_C was superior to that of JPEG2000 and comparable with JPEG-LS. Unlike JPEG-LS, SPACS_C can provide a quality progressive code flow, which means that SPACS_C can also be used in loss compression and can stop coding when a limited bit rate is satisfied. SPACS_C can use part of the code stream to reconstruct the entire image, whereas JPEG-LS can only reconstruct part of the image. Conclusion The proposed method enhances the coding performance of SPC for lossless image compression by decreasing the output of location bit "1". Extensive experiment results show that the lossless compression performance of SPACS_C is better than that of JPEG2000 and comparable with JPEG-LS. The process mode used in SPACS_C suits the low sparseness in the bottom bit planes of wavelet-transformed images. Moreover, SPACS_C can progressively compress images such as JPEG2000. Unlike JPEG-LS, which can only compress images with 8-bit depth, SPACS_C can be used for images with any bit depth.