Y. Wang, T. Orchard, and A.R. Reibman. Multiple description image coding for noisy channels by pairing transform coefficients. In IEEE 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of MD vector quantizers have been proposed [9] 11] 19] 30] and the MD lattice quantizers of [30] do effectively close the gap between the performance of the entropy constrained MD scalar quantizer and the MD rate distortion bound. A rather different approach pioneered by Wang et al. 22] [33] and then extended by Goyal and Kovacevi c [13] consists of applying a suitable blockwise transform to the input vector before coding to obtain the MD property. This approach is usually called MD Transform Coding. The basic idea is to decorrelate the vector components and then to introduce again ....

....two Gaussian components, with the usual assumption that oe 1 oe 2 . Finally the side distortion is given by: oe 1 Gamma oe 2 ) 64) Actually they consider also the case of larger vectors. For the twochannel case their work is an extension of the results presented in [22] [33]. It is interesting to notice that if the Gaussian source has a circularly symmetric probability density, i.e. oe 1 = oe 2 , then the distortion is independent of ae. In this case the side distortion cannot be reduced with the addition of redundancy, so the approach based on correlating ....

Y. Wang, T. Orchard, and A.R. Reibman. Multiple description image coding for noisy channels by pairing transform coefficients. In IEEE 1997.

....Wang and Zhu made a detailed overview of error control and concealment techniques. These techniques can be characterized as follows: 1) Layered coding with transport prioritization, i.e. a combination of scalability layers and error correction codes [2, 12, 21] 2) Multiple description coding [16, 17]; 3) Joint source and channel coding [1] 4) Robust waveform coding, i.e. redundancy in the waveform coding stage [6] 5) Robust entropy coding, which places redundancy in the entropy coding stage [11, 13] 6) Postprocessing at the decoder, which blindly recover the lost pixels based on their ....

Y. Wang, M. T. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by pariing transform coefficients," Proc. IEEE Workshop of Multimedia Signal Processing, Princeton, June 1997.

....design idea, the Scaling Hadamard transform for equal rate channels and the Scaling DST transform for sequential protection channels. 1. INTRODUCTION Multiple Description Coding (MDC) has recently been shown to be effective as a diversity technique for robust communication over erasure channels [2, 3, 4]. The problem of two description coding was first formulated by E1 Gamal and Cover [5] Different MDC systems have since been proposed in the literature, which include the design using a Multiple Description Scalar Quantizer, MDSQ) 6, 3] and the design using a correlating transform [2, 7, 1, 4] ....

.... [2, 3, 4] The problem of two description coding was first formulated by E1 Gamal and Cover [5] Different MDC systems have since been proposed in the literature, which include the design using a Multiple Description Scalar Quantizer, MDSQ) 6, 3] and the design using a correlating transform [2, 7, 1, 4]. In this paper we study a Multiple Description Trans form Coding (MDTC) system as shown in Fig. 1 [8] The input data is first decorrelated using T (e.g. KLT DCT) After quantization, another transform T2 is applied to recorrelate the data which is split over different channels for ....

Y. Wang, M. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by paring transform coeicients," in Proc. IEEE 1997.

....(MDTC) correlation is reintroduced into data stream by applying a second (correlating) transform to the data, as illustrated in Figure 1.3. The eect is similar to that of channel coding. Two basic MDTC approaches for image coding have emerged recently: MDTC using correlating transforms (MDTC CT) [7] and MDTC using frame expansion (MDTC FE) 8] Figure 1.3: Illustration of MDTC using correlating transform The MDTC CT approach of [7] is based on the idea of projecting DCT coe cients onto a dierent set of basis vectors which introduces correlation between them. In particular, the case of two ....

....1.3. The eect is similar to that of channel coding. Two basic MDTC approaches for image coding have emerged recently: MDTC using correlating transforms (MDTC CT) 7] and MDTC using frame expansion (MDTC FE) 8] Figure 1. 3: Illustration of MDTC using correlating transform The MDTC CT approach of [7] is based on the idea of projecting DCT coe cients onto a dierent set of basis vectors which introduces correlation between them. In particular, the case of two descriptions is considered. Let (x 1 ;x 2 ) be a pair of DCT coecients. Such pair is then transformed into (y 1 ;y 2 ) by p 2 2 ....

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Y. Wang, M. T. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by pairing transform coecients," in Proc. IEEE Workshop on Multimedia Signal Proc., pp. 419-424, Princeton, NJ, June 1997.

....is indeed unrecoverable at the receiver. On the other hand, dependencies between transmitted packets facilitate complete or partial recovery in the face of losses. Deterministic dependencies lead to conventional channel coding [19] while statistical dependencies give the techniques proposed in [30] and generalized in [11] The encoding structure considered in this paper combines elements of deter ministic and statistical redundancy. Refer to Fig. 1. We denote the lN valued information to be communicated by : The source vector is represented through a frame expansion with frame operator ....

Y. Wang, M. T. Orchard, and A. R. Reibman. Multiple description image coding for noisy channels by pairing transform coefficients. In Proc. IEEE Workshop on Multimedia Sig. Proc., pages 419424, Princeton, N J, June 1997.

....techniques developed hcrc or in [12] 14] however, to avoid confusion the term multiple description correlating transform (MDCT) is used for the present technique. C. 2 Pairwise correlating transforms A considerably different approach to MD coding was introduced by Wang, Orchard, and Reibman [8]. Instead of using MDSQ to produce two indices that describe the same quantity, the MD character is achieved with a linear transform that introduces correlation between a pair of random variables; quanti zation is treated as secondary. May 25, 2000 Submitted to IEEE Trans. Inform. Th. 10 E ....

....estimates will be used hroughou he paper. The reader is referred o [36] for deails. 13 D1 could be reduced if side decoder i had some information about Xj, i j. This can be accomplished by transmitting not Xi s, but correlated transform coefficients. The simplest possibility, as proposed in [8], is to transmit quantized versions of Y and Y2 given by Since [y y2 ]tc is obtained with an orthonormal transformation and we are using MSE distortion, the distortion in approximating the Xi s equals the distortion in approximating the Y s. The variances of Y and Y2 are both (0 2 o 22) 2, so ....

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Y. Wang, M. T. Orchard, and A. R. Reibman. Multiple description image coding for noisy channels by pairing transform coefficients. In Proc. IEEE Workshop on Multimedia Sig. Proc., pages 41942.

....is extended to many descriptions by applying FEC coding to the output of MD scalar quantizer to generate more than two descriptions. In particular an (n; 1; n) repetition code is presented as a specific example. Correlating transforms are used to introduce redundancy between pairs of values in [82, 88]. This method is based on introducing a statistical redundancy between the pair of values. In [89] quantized overcomplete frame expansions are used to produce a small set of descriptions with some redundancy. In this case, the redundancy is deterministic and is caused by using a larger expansion ....

Y. Wang, M. T. Orchard, and A. Reibman, "Multiple description image coding for noisy channels by pairing transform coefficients," Proceedings IEEE Workshop on Multimedia Signal Processing, 1997, pp. 419--424.

....TX. Please address correspondence to Justin Ridge, e mail: jridge seas.smu.edu. result is achieved irrespective of which description(s) is received. In this paper, MDC refers to coders which adhere to the information theory meaning of multiple descriptions[4] including those presented in [5], 6] and [7] rather than those which, although appearing under the MDC banner, employ statistical channel models[8] The ability of multiple description coding to guarantee an absolute lower bound on quality, even under very lossy conditions, has led to its increasing popularity. However, in ....

....Current multiple description coders[9] 10] approach the optimum by performing non orthogonal transforms on the source data, so that the partitioned streams contain the required correlation. One of the better multiple description coders is the paired transform coefficient MDC introduced in [5] and enhanced in [6] Instead of using a transform which decorrelates all coefficients, transform basis vectors are rotated by some so that correlation between pairs of coefficients remains. Practically, this can be accomplished by rotating the DCT coefficient pair (c 1 ; c 2 ) to give c 1 ....

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Y. Wang, M. T. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by pairing transform coefficients, " in Proc. IEEE Signal Processing Society 1997 Workshop on Multimedia Signal Processing, Princeton, NJ, June 1997.

....Permute bitstream block order Block Partition Channel noise Channel noise Channel noise Fig. 3. Block diagram of smoothed description coder, with refinement feedback path shown as a dashed line. A. MDC reference coder For comparison purposes, we select the multiple descriptions coder of [13], which is equivalent to [5] with = 4. Unless the MDC coder is able to adapt extremely quickly to error bursts, the value of will not accurately reflect the channel during bursts, and thus the actual value assigned to is not of great relevance. Most MDC coders consider only the cases where ....

....accurately reflect the channel during bursts, and thus the actual value assigned to is not of great relevance. Most MDC coders consider only the cases where either one entire description is lost, or both streams are received perfectly; reality is likely to exist somewhere in between. Because [13] uses a block based coder with no inter block dependencies, the performance can be written as a linear combination, Q av = 1 Gamma p) 2 Q 2 2p(1 Gamma p)Q 1 (10) where p is the probability of a block error, and Q i is the average coder performance when i descriptions are received. Note ....

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Y. Wang, M. T. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by pairing transform coefficients, " in Proc. IEEE Signal Processing Society 1997 Workshop on Multimedia Signal Processing, Princeton, NJ, June 1997.

....to different packets so in the case of a packet loss, the lost coefficients can be estimated from the received coefficients. The redundancy comes from the relative inefficiency of scalar entropy coding on correlated variables. This method is a generalization of the technique proposed in [7, 8] for two channels. The second method uses a deterministic redundancy between descriptions, introduced by representing the source data via a frame. That is, we use a frame expansion from C n to C m (m n) as a computationally simple approach to generalized MD coding [9] 2 Multiple ....

....coder could be improved by using a perceptually tuned quantization matrix as suggested by the JPEG standard. Here we have used a constant quantization matrix for simplicity. With this type of tuning it should be possible to design a system which, say, performs precisely as well as the system in [7] when two or four of four packets arrive, but which performs better when one or three packets arrive. A full image communication system requires packetization. We have not explicitly considered this, so we do not produce four streams with precisely the same number of bits. The expected number of ....

Y. Wang, M. T. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by pairing transform coefficients," in Proc. First IEEE SP Workshop on Multimedia Signal Processing, (Princeton, NJ), pp. 419--424, June 1997.

.... Gersho, Witsenhausen, Wolf, Wyner, Ziv and Ozarow in 1979, was to characterize the achievable quintuples (R 1 ; R 2 ; D 0 ; D 1 ; D 2 ) The first design algorithm for practical MD coding was given by Vaishampayan [1] and the first transform based approach was devised by Wang, Orchard, and Reibman [2]. For more background on MD coding, see [1, 3] and the references therein. Describing a source with M packets (descriptions) such that any subset of the packets yields a useful reconstruction is a generalization of the MD problem. We propose the use of linear transforms from R N to R M (with ....

....yields a useful reconstruction is a generalization of the MD problem. We propose the use of linear transforms from R N to R M (with M N) followed by scalar quantization as a computationally simple approach to generalized MD coding. Linear transform approaches for M = N are investigated in [2, 4, 5]. 2 Problem Statement Consider communicating a source taking values in R N across an erasure channel. Denote the channel alphabet by X and suppose jX j = 2 (N=M)R , where M is the number of channel uses per N tuple and R is the overall rate per component (including channel coding) The ....

Y. Wang, M. T. Orchard, and A. R. Reibman. Multiple description image coding for noisy channels by pairing transform coefficients. In Proc. IEEE Workshop on Multimedia Sig. Proc., pages 419--424, Princeton, NJ, June 1997.

....approach was based on scalar quantization with the MD property. Though MD scalar quan M. Vetterli is also with the Univ. of California, Berkeley. tizers can be used in conjunction with transforms [2] the first successful attempts to use transforms to obtain the MD property were reported in [3, 4]. For backgroundon the MD problem, see [1] and the references therein. The aforementioned techniques are specific to the twochannel MD problem where all, half, or none of the bits make it to the decoder. When applied to packet communication with more than two packets, they fail to take full ....

....to different packets so in the case of a packet loss, the lost coefficients can be estimated from the received coefficients. The redundancy comes from the relative inefficiency of scalar entropy coding on correlated variables. This method is a generalization of the technique proposed in [3, 4] for two channels. The coding of a source vector x proceeds as follows: 1. x is quantized with a uniform scalar quantizer with step size Delta: x q i = x i ] Delta , where [ Delta ] Delta denotes rounding to the nearest multiple of Delta. 2. The vector x q = x q 1 ; x q 2 ; x q n ....

[Article contains additional citation context not shown here]

Y. Wang, M. T. Orchard, and A. R. Reibman. Multiple description image coding for noisy channels by pairing transform coefficients. In Proc. IEEE Workshop on Multimedia Sig. Proc., pp. 419--424, June 1997.

....pair of indices with a selectable amount of redundant coding between them. Application of MD scalar quantizers to image coding was considered in [2] including discussion of extensions to more than two descriptions. Correlating transforms are used to introduce redundancy between pairs of values in [3, 4]. In [5] quantized overcomplete frame expansions are used to produce a small set of descriptions with some redundancy. Data partitioning is another technique used to add error resiliency to a source coder (e.g. 6, 7, 8, 9] High performance compression algorithms, such as the SPIHT image coder ....

Y. Wang, M. T. Orchard, and A. Reibman, "Multiple description image coding for noisy channels by pairing transform coefficients," in Proc. IEEE Workshop on Multimedia Signal Processing, pp. 419-- 424, 1997.

....video data into equally important streams such that the decoding quality using any subset is acceptable, and that better quality is obtained by more descriptions. It is assumed in MDC that the probability of losing all the descriptions is small. MDC has been implemented in several ways [8] [9]. A scalar quantizer [8] applies two side scalar quantizers in order to produce two descriptions. In order to minimize reconstruction errors when both descriptions are received, it then maps a proper subset of index pairs formed from side quantizers to central quantizer intervals. The difficulties ....

.... with this approach are that optimal index assignments are hard to achieve in real time, and that suboptimal approaches, such as A2 index assignment [8] introduce a large overhead in bit rate [10] Instead of putting each pixel in every description, a pair wise correlating transform (PCT) [9] approach has been proposed to introduce correlations in each pair of transform coefficients and distribute the two coefficients resulted from PCT into two descriptions. This approach has high coding efficiency when both descriptions are available but has mediocre reconstruction quality with one ....

Y. Wang, M. T. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by pairing transform coefficients," in Proc. IEEE First Workshop Multimedia Signal Processing, June 1997, pp. 419-424.

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Y. Wang, M. T. Orchard, and A. R. Reibman, "Multiple Description Image Coding for Noisy Channels by Pairing Transform Coefficients," Proc. IEEE 1997 First Workshop on Multimedia Signal Processing, (Princeton, NJ), June 1997.

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Y. Wang, M. Orchard, and A. Reibman, "Multiple Description Image Coding for Noisy Channels by Pairing Transform Coefficients," in Proc. IEEE

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Y. Wang, T. Orchard, and A.R. Reibman. Multiple description image coding for noisy channels by pairing transform coefficients. In IEEE 1997.

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Y. Wang, M. T. Orchard, and A. R. Reibman. Multiple description image coding for noisy channels by pairing transform coefficients. In Proc. Workshop on Multimedia Signal Processing, pages 419--424. IEEE, Princeton, NJ, June 1997.

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Y. Wang, M.T. Orchard, and A.R. Reibman, "Multiple description image coding for noisy channels by pairing transform coefficients," in Proc. IEEE Workshop on Multimedia Signal Processing, Princeton, NJ, June 1997, pp. 419-424.

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Y. Wang, T. Orchard, and A.R. Reibman. Multiple description image coding for noisy channels by pairing transform coefficients. In IEEE 1997.

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Y. Wang, M. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by paring transform coefficients," in Proceeding IEEE 1997 First Workshop on Multimedia Signal Processing, MMSP-97, (Princeton, N J), June 1997.

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Y. Wang, M. Orchard, and A. Reibman, "Multiple description image coding for noisy channels by pairing transform coefficients," in Proceedings of IEEE Signal Processing Society Workshop on Multimedia Signal Processing, (Princeton, N J, USA), Jun 1997.

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Y. Wang, M. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by paring transform coefficients," in Proc. IEEE 1997 First Workshop on Multimedia Signal Processing, 1997.

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Y. Wang, M. T. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by pairing transform coefficients;' in Proc. IEEE Workshop on Multimedia Signal Proc., pp. 419-424, June 1997.

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Y. Wang, M. T. Orchard, and A. R. Reibman, "Multiple description image coding for noisy channels by pairing transform coefficients," in Proc. IEEE Workshop on Multimedia Signal Proc., pp. 419-424, Princeton, N J, June 1997.

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