基于离散Hermite多项式的图像压缩

Image Compression Based on Discrete Hermite Polynomials

图像压缩编码能有效地减少图像像素间的信息冗余,并同时保证图像重构质量和较低的计算复杂度。基于变换域的图像压缩编码是目前最常用且性能最优的压缩技术之一,但基于离散正交多项式变换的图像压缩方法还未被深入研究。在研究JPEG的编码解码流程基础上,提出基于离散Hermite多项式的图像压缩算法,通过变换核的信息熵与DCT变换核的信息熵比值确定量化表,最后对量化结果进行熵编码,最终实现了基于离散Hermite多项式的图像压缩和重建全过程。与主流的图像压缩标准JPEG进行了比较,实验结果表明,两种算法的压缩率相似,性能相近,压缩后图像的PSNR相差很小。

Image compression can effectively decrease information redundancy among image＇s pixels,and also ensure its reconstruction quality and lower computation complexity. The transform domain image compression coding is the most commonly used and one of the most optimal compression technology, but the image compression methods based on discrete orthogonal polynomials transform have not yet been deeply studied. Through studying the procedures of encoding and decoding of JPEG,we proposed an image compression algorithm based on discrete Hermite polynomials. Quantization table was determined depending on the ratio of the information entropy of the transform core and that of DCT. At last the results of quantization were encoded by using Huffman entropy coding. We realized the whole process of image compression and reconstruction based on discrete Hermite polynomials. The experimental results show that the algorithms are of similar compression ratio, share similar performance and the difference in peak signal noise ratio（PSNR） is small compared with the mainstream JPEG image compression standard.