Study On Image Compression Using Discrete Orthogonal Polynomials Transform

The transform domain based image compression coding is one of the most commonly used and the best performed compression technologies, the mainstream algorithms such as JPEG, JPEG 2000, JPEG XR etc. The transform principal of discrete orthogonal polynomials can be thought that the original signals are projected into the kernel functions using a set of orthogonal polynomials. The projected signals have low redundancies and belong to the typical orthorgonal transform. However, the image compression method based discrete orthogonal polynomials transform has not yet been deeply studied. Regarding the above issues, this thesis studies lossy and lossless image compression based on discrete orthorgonal polynomials transform. The research achievements as follows:1. This thesis proposes a lossless image compression scheme based on integer discrete Tchebichef orthogonal polynimials transform(integer DTT). By the method of matrix factorization, and factorizing the ? discrete Tchebichef basis transform matrix into +1 single-row elementary reversible matrices(SERMs) with minimum rounding errors to achieve the linear transform from integer to integer mapping. Experimental results evaluated on three public databases of image compression show that the proposed algorithm has superior compression performance when compared with integer discrete cosine transform(integer DCT). And in the vast majority of color image tests indicate that the compression efficiency of integer DTT is better than that of presently international lossless image compression standard JPEG-LS(JPEG Lossless/near-lossless compression Standard).2. An image compression scheme based on discrete Tchebichef polnomials and soft decision quantization is proposed. This thesis studies the distribution of the transform coefficients of DTT by the approach of KS test statistic and designs the optimized quantization table based DTT by taking advantage of soft decision quantization to optimize the rate distortion for the purpose of improving reconstruction quality. Compared with the mainstream DCT image compression method, experimental results show that the proposed algorithm is of greater reconstruction image quality when the bit ratio exceeds 0.5bpp. The bit ratio is decreased by 0.25 bpp, 0.49 bpp, 0.20 bpp when peak signal-to-noise-ratio(PSNR) is 35 dB, 40 dB, 45 dB respectively. Meanwhile, they are similar on the elapsed time in encoding and decoding.3. From studying the procedures of encoding and decoding of JPEG, this thesis proposes an image compression algorithm based discrete Hermite orthogonal polynomials transform. Determining quantization table depends on the ratio of the information entropy of discrete Hermite transform(DHT) core and that of DCT. Last, encode the quantized results by using Huffman entropy coding. The experimental results show that the algorithm is of similar compression performance and the difference in PSNR is little when compared with the mainstream DCT image compression method.