A three-layer scheme for M-channel multiple description image coding

Abstract

A three-layer scheme is developed for M-channel multiple description image coding. In each description, a subset of the source is encoded in the first layer. In the second layer, the remaining subsets are encoded sequentially by predicting from the already encoded subsets. Each description can thus produce a coarse reconstruction of the source. When multiple descriptions are received, a refined reconstruction is obtained by fusing all coarse reconstructions. A third layer is further included to refine the reconstruction when only one description is lost, which dominates when the probability of channel error is low. We first derive the closed-form expressions of the expected distortion of the system for 1-D sources. The proposed scheme is then applied to lapped transform-based image coding, where we formulate and obtain the optimal lapped transform. Image coding results show that the proposed method outperforms other latest schemes.

Introduction

Multiple description coding (MDC) addresses the packet losses in a communication network by sending several descriptions of the source such that the reconstruction quality improves with the number of received descriptions [1].

The MDC with two descriptions (or channels) has been studied extensively. Some representative practical designs include the multiple description scalar quantizer (MDSQ) and the pairwise correlating transform [2], [3]. In this paper, we focus on MDC with more than two descriptions, which is more useful in practice. Information-theoretic analyses of this case can be found in, e.g., [4], [5], [6]. Among them, an achievable rate-distortion (R-D) region for the MDC of memoryless sources is given in [4], by generalizing the two-description result in [7]. An improved achievable region is obtained in [5] by encoding a source in M stages, where the k-th stage refines the previous stages and can only be decoded when more than k descriptions are received. The scheme is based on the theory of source coding with side information and distributed source coding (DSC) [8]. Recently, another improved scheme is developed in [6], which can achieve points outside the achievable region in [5]. However, these information-theoretic schemes cannot be directly applied in practices, due to their high encoding and decoding complexities, particularly the lack of structured codes to implement the binning scheme.

Various practical designs of M-channel MDC have also been developed. In [9], [10] erasure correcting codes are used to provide unequal loss protections (ULP) to different layers of the output of a scalable coder. Fast ULP algorithms have been studied in, for example, [11], [12]. However, many existing block transform-based coders are either not scalable or only have very limited granularity of scalability, such as JPEG, H.264 and the latest JPEG-XR image coding [13], [14]. Therefore the ULP-based MDC may not be optimal in these cases, and it is necessary to develop alternative MDC schemes for these applications that can take full advantage of the underlying coders.

In [15], the MDSQ in [2] is extended to more than two channels via a combinatorial optimization approach. However, the scheme only has one degree of freedom and only assigns the index symmetrically around the main diagonal of the index matrix. The most general M-channel symmetric MDC has M−1 degrees of freedom, which maximize the flexibility in tuning the redundancy. Another extension of the MDSQ with M−1 degrees of freedom is developed in [16], which shares some similarities to the method in [5], i.e., the coding consists of multiple stages such that each stage refines the preceding stages. However, both the algorithms in [15], [16] become quite complicated as the increase of the number of descriptions.

A lattice vector quantization-based MDC method is presented in [17], where M descriptions are generated by uniquely assigning each point in a finer central lattice to M points in a sublattice. The method also involves an index assignment problem, which increases the complexity in design and implementation.

In another class of MDC methods, the source splitting scheme in [18], [19] is generalized. In [20], the transform coefficients are split into two subsets, and each is quantized into one description. Each description also includes the coarsely quantized result of the other subset, which improves the reconstruction when the other description is lost. Recently the method in [20] is generalized to JPEG 2000 in [21] for two-description coding, denoted as RD-MDC, where each JPEG 2000 code-block is coded at two rates, one in each description. In [22], the RD-MDC in [21] is extended to M-channel case, where each JPEG 2000 code-block is still encoded at two rates. The higher-rate coded code-blocks are divided into M subsets and are assigned to M descriptions. Each description also carries the lower-rate codings of the remaining code-blocks. One benefit of [21], [22] is that they maintain a good compatibility with JPEG 2000, e.g., each description can be decoded by a standard JPEG2000 decoder. In [23] a multi-rate method, which generalizes the two-rate method in [22], is developed. The method in [23] exploits the redundancy more efficiently than in [22]. However, its complexity increases rapidly with the number of descriptions.

In [24], a modified MDSQ (MMDSQ) is developed, where the quantization bins in the base layers of the two descriptions are staggered to each other. This creates a refined central quantizer when both descriptions are available. The quantization error of the central quantizer is further encoded and split into the second layers of two descriptions. In [25], a two-rate coding method is proposed for M-channel MDC, where the lower rate coding also uses staggered quantization, similar to the MMDSQ. The method in [25] also exploits the residual correlations in the source using a specially designed predictive encoder. Another improvement of the MMDSQ is investigated in [26], where the second layer can be used to reduce the side distortion. In [27], the scheme in [26] is applied to MD image coding, where the first layers are obtained by rotating the image by different angles before encoding. The reconstructions from the first stage are averaged, and the error is encoded and split to the second stages of all descriptions. However, this method only has one degree of freedom, and its theoretical performance for $M>2$ is unknown.

In [28], a prediction compensated MDC scheme (PCMDC) is developed for the two-channel case, where the source is partitioned into two subsets, and each subset is encoded as the base layer of one description. Each description also encodes the prediction residual of the other subset, using the reconstruction of the base layer as the prediction reference. This is more efficient than the two-rate coding in [20], [21]. When applied to the time-domain lapped transform-based image coding [29], PCMDC achieves better results than those in [24], [21], and represents the state of the art in two-description image coding.

In this paper, motivated by the superior performance of the two-channel PCMDC in image coding, we generalize the prediction-compensated approach to M-channel case and develop a three-layer MDC (TLMDC) algorithm. In the first layer of each description, a subset of the source samples is encoded. In the second layer, the remaining subsets are encoded sequentially by predicting from the already encoded subsets. As a result, the first two layers can generate a coarse reconstruction of the source. When multiple descriptions are received, a refined reconstruction is obtained by fusing all coarse reconstructions. Moreover, when only one description is lost, a further refinement can be obtained, which also occurs the most frequently among all error scenarios when the loss probability of each description is very small.

The organization of the paper is as follows. In Section 2, we describe the framework of the proposed scheme, and derive the closed-form expression of the expected distortion of the proposed scheme for 1-D Gaussian sources. In Section 3, we modify our scheme for lapped transform-based MD coding, and formulate the optimization of the corresponding lapped transform. In Section 4, the performance of the proposed method in MD image coding is demonstrated and compared with other methods.