This chapter provides a brief introduction about the fundamentals of image compres- sion and information theory. The fidelity criteria for evaluating the quality of decoded images is discussed. A brief introduction to JPEG image compression and embedded image compression is presented. The background and scope of the work, the motiva- tion and the objective of the thesis are systematically discussed. A brief chapter wise description has been also presented.
Compression Performance
Assessment of Discrete Tchebichef
Transform
Preview
The Discrete Tchebichef Transform (DTT) based on orthogonal Tchebichef polyno- mials can be an alternative to Discrete Cosine Transform (DCT) for JPEG image compression standard. The properties of DTT are not only very similar to DCT, but it has also higher energy compactness and lower computational advantage using a set of recurrence relation. Through extensive simulation, image reconstruction accuracy (i.e., PSNR and MSSIM) and the compression performance at various scaling factors for both DCT and DTT is verified. It has been demonstrated that DTT exhibit better PSNR/MSSIM performance than DCT for images having higher intensity gradation. DTT shows nearly similar PSNR/MSSIM performance with DCT for smooth and textured images. It is also further verified that DTT has better compression ability than DCT in most of the images.
A DTT based hybrid embedded coder has been proposed for image compression applications. In this coder, DTT is coupled with Set partitioning in hierarchical coding techniques (SPIHT). Further, human visual system (HVS) with appropriate perceptual weights are applied to improve the perceptual quality of the reconstructed image. The compression and image reconstruction performance has been compared with some the state-of-the-art coders in the literature. Extensive simulations on various kinds of images indicates strongly that the proposed coder outperforms most of the coders.
A fast zigzag pruning DTT algorithm of different prune lengths has been pro- posed and compared with the existing DTT fast algorithms. The principal idea of the proposed algorithm is to make use of the distributed arithmetic and symmetry
property of 2-D DTT, which combines the similar terms of the pruned output. Nor- malization of each coefficient has been done by merging the multiplication terms with the quantization matrix so as to reduce the computation. Equal number of zigzag pruned coefficients and block pruned coefficients are used for comparison to test the efficiency of our algorithm. Experimental method shows that the proposed method is quite competitive with the block pruned method. Specifically for 3 × 3 block pruned case, the proposed method provides lesser computational complexity and has higher peak signal to noise ratio (PSNR). The reconstructed image quality of different pruned length is evaluated both subjectively and objectively. The proposed method has been implemented on a Xilinx XC2VP30 FPGA.
2.1
Introduction
Image Transform methods using orthogonal kernel functions are commonly used in im- age compression. One of the most widely known image transform method is Discrete Cosine Transform (DCT), used in JPEG compression standard [4].The computing de- vices such as Personal digital assistants (PDAs), digital cameras and mobile phones require a lot of image transmission and processing. Therefore, it is essential to have efficient image compression techniques which could be scalable and applicable to these smaller computing devices. Discrete Tchebichef Transform (DTT) which is derived from a discrete class of popular Tchebichef polynomials is a novel orthonormal version of orthogonal transform. It has found applications on image analysis and compression [45],[49].
Though various efficient compression techniques have been reported, the wide range of multimedia applications demands for further improvement in compression quality. Therefore, most of the research activities are focused on wavelet based coders rather than DCT based image coders. Wavelet based coders offers superior perfor- mance in terms of visual quality and PSNR at very low bit rates (below 0.25 bpp) [15],[16],[79],[80]. This is mainly attributed due to innovative strategies of data orga- nization and representation of wavelet transformed coefficients.
Although wavelets are capable of more flexible space-frequency resolution trade offs than DCT, DCT is still widely used in many practical applications because of its compression performance and computational advantages. Recently, DCT-based coders with innovative data organization strategies and representations of DCT coef- ficients have been reported with high compression efficiency [39]- [43].
Recently, DTT has found excellent rate-distortion trade-off like DCT and outper- forms DCT for image having high intensity gradations [48],[81]. Therefore, DTT is
used as a substitute for DCT in an embedded coder. Further, human visual system (HVS) has been applied to increase the subjective quality of the image [82]. The proposed embedded coder consists of HVS with DTT and SPIHT coding techniques. The performance of this kind of coder has been evaluated and compared with DCT based embedded coders, JPEG, improved JPEG [83], Significance tree quantization (STQ) [40], and STQ+Haar.
The Tchebichef moment compression that has been proposed in this dissertation is meant for smaller computing devices owing to its low computational complexity [51]-[53]. Ishwar et al. [52] have shown that DTT has lower complexity since it requires the evaluation of only algebraic (only add and shift operations, no multipli- cations) expressions, whereas implementation of DCT requires integer approximation or intermediate scaling, like Integer cosine transform (ICT) [37].
There are many DCT compression algorithms which can be computed in a fast way by means of direct or indirect methods [84]-[86]. These algorithms assume same number of input and output points. However, in image coding applications, the most useful information about the image data is kept in the low-frequency DCT coefficients. Therefore, only these coefficients could be computed. This gives rise to the application of pruning techniques. Additional processing speed-up is also possible using this idea. Several algorithms for pruning the 1-D DCT in [54]-[58] and 2-D DCT in [59]-[62] have been addressed.
A 2 × 2 block pruned out of 4 × 4 DTT algorithm which computes the upper left quarter of 4 ×4 image blocks has proposed in [53]. Saleh [87] has proposed a fast 4×4 algorithm suitable for different block sizes. Having surveyed on different DCT pruning algorithms, a fast zigzag pruning algorithm and its image reconstruction quality for image coding applications have been proposed.