V.K. Goyal, J. Kocevic, R. Arean, and M. Vetterli. Multiple Description Transform Coding of Images In Proceedings of ICIP, 1998  Home/Search   Document Details and Download   Summary   Related Articles   Check

....mutually refinable information. Therefore, the quality of the recovered signal is dependent only on the number of received descriptions, and not on the specific loss pattern. Many methods have been proposed for the generation of MD, among which MD scalar quantization [2] correlating transforms [3] and so on. With some modifications these methods can be used to insert redundancy in spatial localized fashion so that a given region of interest (ROI) is more protected against packet losses. However, these methods are not compatible with standard image video co decoding tools; therefore their ....

V. Goyal, G. Kovacevic, R. Arean, M. Vetterli, "Multiple description transform coding of images", in International Conference on Image Processing, Chicago, Illinois, USA, Oct. 1998

....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 ....

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V. K. Goyal, J. Kovacevic, R. Arean, and M. Vetterli, "Multiple description transform coding of images," in ICIP'98, 1998.

....each corresponding to one of the possible loss scenarios. In an ideal MDC channel environment, the channels are independent and data on each channel is either completely lost or received intact. This environment has been studied extensively both theoretically, 6] 7] and practically, 8] [9], 10] 11] 12] etc. The paper by Goyal [5] provides a good overview of MDC systems. Figure 1 Generic MDC system. The source is encoded in two descriptions, S 1 and S 2 . They are transmitted through the network over different channels. At the decoder, if only one description is received, ....

V.K. Goyal, J. Kovacevic, R. Arean and M. Vetterli. "Multiple Description Transform Coding of Images". IEEE International Conference on Image Processing (ICIP98), Chicago, IL, October 1998

....set. Finally, section 6 compares the proposed approach with MDS codes which are optimal when only the overweight factor is considered. 2 Robustness and multiple description As already presented in the introduction, solutions to the multiple description problem did appeared several years ago. In [3], the generic solution is decomposed into 3 fundamentals steps. First an orthogonal transform (DCT) is applied to the initial signal to roughly decorrelate each sample. The obtained coefficients are partially recorrelated with a known unitary transform to add a statistical redundancy (with ....

....coding is eventually implemented for each new description as step 3. The known transform can be a rotation of angle # as proposed in [4] Each elements of a description result of pairing decorrelated and quantized coefficient in the two channels case. To extend this result for the N channels case, [3] uses a cascading of several transforms. Vaishampayan [5] constructs descriptions from coefficients index located in a band matrix. One example of index assignment is shown at figure 1. If both descriptions arrived to destination, initial quantization is reconstructed. Otherwise, if one ....

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V. K. Goyal, J. Kovacevic, R. Arean, and M. Vetterli, "Multiple description transform of coding images," in Proc. IEEE Int. Conf. Image Processing, Chicago, IL., 1998.

....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 descriptions is considered. Let (x 1 ;x 2 ) ....

....description, and estimation error is independent of which description is received [7] i.e. descriptions are equally important. The angle of 45 was chosen to produce balanced descriptions, in the sense that both descriptions have equal energies and require the same bit rate. MDTC FE approach [8] is based on a slightly dierent idea. Rather than modifying the set of basis vectors (e.g. by rotation, as in MDTC CT above) the basis set is expanded beyond the dimensionality of the vector space under consideration. A simple illustration is given in Figure 1.4. The left plot in Figure 1.4 shows ....

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V.K.Goyal,J.Kova cevi c, R. Arean, and M. Vetterli, "Multiple description transform coding of images," in Proc. IEEE Int. Conf on Image Proc. (ICIP'98 ), Chicago, IL, Oct. 1998.

....considered the case of two descriptions. Theoretical results for the achievable rate region include results in [44, 79] Currently the achievable rate distortion is completely known only for the two channel memoryless Gaussian source. Recent work in the area of multiple descriptions includes [80, 81, 82, 83, 84, 85, 86, 87]. Previous work on MD coding includes methods which allow a wide range of redundancy levels to be introduced across a small set of descriptions (usually two descriptions) The MD scalar quantizer in [45] uses an index assignment to map a regular quantizer index to a pair of indices with a ....

....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 ....

V. K. Goyal, J. Kovacevic, R. Arean, and M. Vetterli, "Multiple description transform coding of images," Proceedings International Conference on Image Processing, vol. 1, 1998, pp. 674--678.

....encoding by defining four scalability modes: spatial scalability, temporal scalability, data partitioning, and SNR scalability [7] 8] A combination of the scalability modes leads to the hybrid scalability consisting of a large number of layers. ffl The non cumulative layering approach [2] [6] In this approach, the video is encoded in two or more independent layers. Each layer is independently decodable and provides improvements to the video reception quality. Each receiver can join any subset of the video layers without joining the layer 1 multicast group. Multiple description ....

V. K. Goyal, J. Kocevi'c, R. Arean, and M. Vetterli, "Multiple description transform coding of images," Proceedings of ICIP, Chicago, IL, Oct. 1998.

....the bitstream useless to the decoder) the MD stream is insensitive to them and thus has the desired feature that the delivered quality is dependent only on the fraction of packets delivered reliably. While most of the initial work in this area has focused on the special case of descriptions [4] [5], there has been recent interest in the case also [6] 9] For example, 9] presents an efficient algorithm that transforms an MR based prioritized bitstream into a nonprioritized MD packet stream. The proposed strategy uses a purely channel coding based paradigm based on forward error correction ....

....a nonprioritized MD packet stream. The proposed strategy uses a purely channel coding based paradigm based on forward error correction (FEC) channel codes and exhibits a departure from traditional signal processing based approaches that employ scalar quantizers, correlating transforms etc. 4] [5] to approach the MD problem. It incorporates the Priority Encoding Transmission (PET) 10] philosophy in formulating a systematic, fast and end to end rate distortion optimized algorithm. Details of this are presented in Section II. The smart end hosts simple network philosophy which has ....

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V. K. Goyal, J. Kov aevic , R. Arean, and M. Vetterli, "Multiple description transform coding of images," in Proc. IEEE Int. Conf. Image Processing, vol. 1, Chicago, IL, Oct. 1998, pp. 674--678.

....between redundant code and single description quality must be realized. The degree to which the importance of one of these is elevated over the other becomes the weighting in the joint optimization problem[6] A. Correlation between MDC descriptions 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 ....

V. K. Goyal, J. Kovacevi'c, R. Arean, and M. Vetterli, "Multiple description transform coding of images," in Proc. IEEE Conference on Image Processing, Chicago, IL, October 1998, pp. 674--678.

....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 ....

V. Goyal, J. Kovacevic, R. Arean, and M. Vetterli, "Multiple description transform coding of images," in Proc. ICIP 98, 1998.

....the bitstream useless to the decoder) the MD stream is insensitive to them and thus has the desired feature that the delivered quality is dependent only on the fraction of packets delivered reliably. While most of the initial work in this area has focussed on the special case of N = 2 descriptions [4, 5], there has been recent interest in the N 2 case also [6, 7, 8, 9] For example, 9] presents an e#cient algorithm that transforms an MR based prioritized bitstream into a non prioritized MD packet stream. The proposed strategy uses a purely channel coding based paradigm based on Forward Error ....

....and exhibits a departure from 2 There has been considerable e#ort for instance, within the MPEG 4 video coding standard on the issue of supporting Fine Granular Scalability (FGS) 3] 2 traditional signal processing based approaches that employ scalar quantizers, correlating transforms etc. [4, 5] to approach the MD problem. It incorporates the Priority Encoding Transmission (PET) 10] philosophy in formulating a systematic, fast and end to end rate distortion optimized algorithm. Details of this are presented in Section 2. The smart end hosts dumb network philosophy which has enabled ....

[Article contains additional citation context not shown here]

V. K. Goyal, J. Kovacevic, R. Arean, and M. Vetterli. Multiple Description Transform Coding of Images. Proceedings of the IEEE International Conference on Image Processing, 1:674--678, October, Chicago, IL, 1998.

....LC uses a hierarchical, decorrelating decomposition, whereas MDC uses a non hierarchical, correlating decomposition. Some approaches that have been proposed for accomplishing such decomposition include overlapping quantization [ 27 ] correlated predictors [ 28 ] correlating linear transforms [ 29 , 30 ], correlating filter banks [ 31 ] and interleaved spatial temporal sampling [ 32 , 23 ] The last approach is known as video redundancy coding in H.263. 17 B. Decoder Error Concealment Decoder error concealment refers to the recovery or estimation of lost information due to transmission ....

V. K. Goyal, J. Kovacevic, R. Arean and M. Vetterli, Multiple description transform coding of images," IEEE Int. Conf. Image Proc. (ICIP98), (Chicago, IL), Oct, 1998. Vol. 1, pp. 674-678.

....For the case of N = 2 and symmetric channels, a closed form solution was obtained for the optimal transform. They also proposed to generate N 2 descriptions by cascading 2 Theta 2 transforms. Goyal et al. also explored the use of over complete frame expansions for accomplishing MDC [13], where a N Theta K (N K) linear transform is used to generate N descriptions. In the remaining sections of this paper, Section 2 formally defines the concept of redundancy and introduces the RRD curve as a performance measure for MDC. Section 3 describes the general framework of using ....

V. K. Goyal, J. Kovacevic, R. Arean and M. Vetterli, "Multiple description transform coding of images," Proc. IEEE Int. Conf. Image Proc. (ICIP98), (Chicago, IL), Oct, 1998.

.... pioneered by Wang, Orchard, and Reibman, MD quantizers are constructed by separately describing (i.e. quantizing and coding) the N coefficients of an N Theta N block linear transform, which has been designed to introduce a controlled amount of correlation between the transform coefficients [5, 6, 7]. In the third approach, pioneered by Goyal, Kovacevi c, and Vetterli, MD quantizers are constructed by separately describing the N coefficients of an overcomplete N Theta K tight frame expansion [8, 7] The present paper contributes to this last category. For completeness, it should be mentioned ....

.... designed to introduce a controlled amount of correlation between the transform coefficients [5, 6, 7] In the third approach, pioneered by Goyal, Kovacevi c, and Vetterli, MD quantizers are constructed by separately describing the N coefficients of an overcomplete N Theta K tight frame expansion [8, 7]. The present paper contributes to this last category. For completeness, it should be mentioned that a number of other papers take yet a fourth approach, in which the natural correlation between symbols is exploited for reconstruction. For example, odd pixels can be predicted from even pixels, and ....

[Article contains additional citation context not shown here]

V. K. Goyal, J. Kovacevi'c, R. Arean, and M. Vetterli. Multiple description transform coding of images. In Proc. Int'l Conf. Image Processing, Chicago, IL, October 1998. IEEE.

....packets, have the drawback of higher latency and are difficult to scale [6, 4] Additionally, since packet loses generally occur during congestion, these requests and subsequent retransmissions can make matters worse. Robustness to data loss can be achieved using multiple description coding (MDC) [23, 29, 16]. MDC coders build correlation between the symbols allowing for good reconstruction from subsets of the data. Much of the previous work has dealt with two channel coding [23] which can withstand the loss half of the transmitted data. There has also been some preliminary work on many channel ....

....MDC coders build correlation between the symbols allowing for good reconstruction from subsets of the data. Much of the previous work has dealt with two channel coding [23] which can withstand the loss half of the transmitted data. There has also been some preliminary work on many channel coding [16, 29]. One can think of the NAIVE encoding as an extreme example of MDC, where no decorrelating transform is applied to the original pixel data, and pictures can be reconstructed from any received data. The algorithm we propose bears many resemblences to work in error concealment [3, 11, 34, 31] ....

V. K. Goyal, J. Kovacevic, R. Arean, and M. Vetterli. Multiple description transform coding of images. Proc. IEEE Int. Conf. Image Processing, October 1998.

....paper seems suitable for this task. 43 It is precisely in the context of image communication that Wang, Orchard and Reibman introduced correlating transforms for MD coding; their image coding results appear in [8] m Image coding results using the generalized framework presented here appear in [13]. These experiments indicate the expected behavior: At the expense of a slight increase in bit rate, image representations can be made robust to packet losses. Conventional channel codes adding such a small amount of redundancy are not as effective. B. Application to Audio Coding As a second ....

V. K Goyal, J. Kovaevid, R. Arean, and M. Vetterli. Multiple description transform coding of images. In Proc. IEEE Int. Conf. Image Proc., volume 1, pages 674478, Chicago, October 1998.

....can be computed in polynomial time for any e. 4 Applications In this section, we give examples of the MDTC applied to robust audio as well as robust image transmission systems. They are meant to illustrate the potential of the proposed method; for more details, the reader is referred to [15, 16]. 1 For m k, a better estimate can be found by exploiting the boundedness of the quantization error [13, 14] 2 Extensions to where Phi 0 is not a frame are suggested by [10] 3 Better reconstructions are possible when the boundedness of the quantization error is exploited [13, 14] 4.1 ....

V. K Goyal, J. Kovacevi'c, R. Arean, and M. Vetterli, "Multiple description transform coding of images," in Proc. IEEE Conf. on Image Proc., (Chicago, IL), October 1998.

....of smaller packets. Creating multiple descriptions of a video signal tting into these small packets having the mutual re nability property is ideally matched to transmission over a network without any form of prioritization among packets. MD coding of still images has been considered recently in [4, 6, 17, 24]. Extensions to video coding have been considered in [14, 15] in the context of subband coding) and in [10, 22] in the context of predictive coding) 4.2 Predictive Multiple Description Coding with Feedback A nontrivial problem in the design of predictive MD video coders is that of encoding ....

V. K. Goyal, J. Kovacevic, R. Arean, and M. Vetterli. Multiple Description Transform Coding of Images. In Proc. IEEE Int. Conf. Image Proc. (ICIP), Chicago, IL, 1998.

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V.K. Goyal, J. Kocevic, R. Arean, and M. Vetterli. Multiple Description Transform Coding of Images In Proceedings of ICIP, 1998

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V.K. Goyal, J. Kocevic, R. Arean, and M. Vetterli. Multiple Description Transform Coding of Images In Proceedings of ICIP, 1998

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V. K. Goyal, J. Kovacevi'c, R. Arean, and M. Vetterli. Multiple description transform coding of images. In Proc. Int'l Conf. Image Processing, Chicago, IL, October 1998. IEEE.

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V. K. Goyal, J. Kovacevic, R. Arean, and M. Vetterli, "Multiple description transform coding of images," in Proceeding of ICIP-98, (Chicago, IL), Oct 1998.

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V. K. Goyal, J. Kovacevic, R. Arean, and M. Vetterli, "Multiple description transform coding of images," in ICIP'98, 1998.

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V. K. Goyal, J. Kovaevi6, R. Arean, and M. Vetterli, "Multiple description transform coding of images;' in Proc. IEEEICIP'98, pp. 674-678, Oct. 1998.

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V. K. Goyal, J. Kovaevi6, R. Arean, and M. Vetterli, "Multiple description transform coding of images," in Proc. IEEE Int. Conf on Image Proc. (ICIP'93), Chicago, IL, Oct. 1998.

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