In this chapter, a novel scheme for generalized MUDC resulting in joint decoding of descriptions with balanced and unbalanced rate-distortion performances was presented. The hierarchically defined MDSQs are used in the proposed frame- work by the successive refinement of the central quantizers. The main parameters involved in MUDC were the central quantizer refinement factor, a and the in- dex assignment matrix parameter gm for the mth MDSQ in the hierarchy. The sufficient and necessary conditions for meeting the required rate-distortion con- straints were proposed for single and joint decoding of descriptions from two MDSQs, m = j and m = k, where k > j, as a > 1, ak−jg
j > gk and ak−j ≥ gk. The proposed conditions are also verified by demonstrating the PSNR increment for different combinations of parameter values. It is observed that at the same rate, the unbalanced joint decoding gives 1.1 dB better performance than the balanced joint decoding.
An efficient realization of the scheme was also shown by using the successive side quantizer bin merging of the initial MDSQ. The rate-distortion performance for joint decoding of N = 2 descriptions has shown that the unbalanced descriptions coming from different MDSQs resulted in superior performance compared to the balance descriptions coming from the same MDSQ. It is also shown that the quality scalability can be achieved if the joint decoding descriptions are selected from different levels and branches of the SSQBM tree. The flexibility to add and remove redundancy in terms of number of descriptions is also achieved by using SSQBM tree structure.
Chapter 4
Multiple Description Scalar
Quantizer with Successive
Refinement
This chapter focuses on achieving quality scalability in MDC framework by suc- cessive refinement of the individual description. The proposed method for achiev- ing quality scalability starts with MDSQ-based MDC for the base layer and then successively refines the side quantizer to design a new framework called MDSQ- SR. The objective of the MDSQ-SR design is to improve the distortion for every refinement layer of a side description when individually decoded and for any combination of levels of refinement of the two refined side descriptions for joint decoding. The rest of the chapter is organized as follows: An overview of the scalable MDC scheme is presented in Section 4.1. The MDSQ-SR design, its dis- tortion constraints and proposed conditions for successful decoding are presented in Section 4.2. Simulation results using the proposed scheme under both balanced and unbalanced description scenarios with application to quality scalable image coding are shown in Section 4.3 followed by the summary in Section 4.4.
4.1
Background
The emergence of using the wavelet transform in image coding has resulted in incorporating extra features, such as scalable decoding into image coding algo- rithms. As scalable coding usually uses hierarchical representations of spatial- quality coding layers with progressive interdependencies, any error in lower lay- ers, for example in low frequency subbands, can propagate into the higher layers. Therefore, in scalable coding, low spatial-quality layers need to be highly pro- tected for channel errors. In addition to hierarchical channel coding strategies, MDC can also be used to make scalable coded bit stream robust. One such exam- ple includes EMDSQ, where a set of side quantizers generating two descriptions are derived from an embedded central quantizer [53, 54]. Other examples either avoid using MDSQ [106] or use MDSQ only as the base layer in an MDC system with a single enhancement layer [107].
Early MDSQ algorithms focussed on obtaining descriptions with balanced rate- distortion performance. In Chapter 3 the conditions for obtaining unbalanced descriptions and their joint decoding are derived and also these conditions are extended for creating more than two descriptions for MDC. In this chapter, in- spired from the results of MUDC scheme, a framework for successive refinement of side quantizers of the MDSQ is formulated to obtain progressive quality update for side quantizers.
In contrast to EMDSQ, the MDSQ-SR design considers different index assignment matrices (resulting into non-overlapped and overlapped side quantizer bins) to incorporate different amounts of redundancy between the descriptions at the base layer. The side quantizer bins of the base layer are then successively refined to guarantee the individual and joint distortion reduction for the enhancement layers. Using different index assignment matrices at the base layer facilitates the user to incorporate different amounts of redundancy among the descriptions depending on the number of diagonals filled in the index assignment matrix. The amount of redundancy among the descriptions for each enhancement layer is controlled by the refinement factor of the side quantizer bins. In MDSQ-SR design, different strategies for quantizer bin index assignments, such as staggered index assignment resulting in non-overlapped side quantizer bins and modified
Figure 4.1: Embedded quantizer for three levels P = 3.
nested index assignment resulting in overlapped quantizer bins are considered. This chapter presents the conditions that the side quantizer bin sizes and the refinement factors have to meet in order to ensure progressive quality increments for a given side quantizer set, as well as for the central quantizer that corresponds to joint decoding scenarios.