Multiple description discrete cosine transform-based ...

Multiple description discrete cosine transform-based image coding using DC coefficient relocation and AC coefficient interpolation Nafees Mansoor A. K. M. Muzahidul Islam M. Abdur Razzak

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Journal of Electronic Imaging 22(2), 023030 (Apr–Jun 2013)

Multiple description discrete cosine transform-based image coding using DC coefficient relocation and AC coefficient interpolation Nafees Mansoor A. K. M. Muzahidul Islam Universiti Teknologi Malaysia Malaysia Japan International Institute of Technology Department of Electronic Systems Engineering 54100, Jalan Semarak Kuala Lumpur, Malaysia E-mail: [email protected] M. Abdur Razzak Independent University, Bangladesh School of Engineering and Computer Science Department of Electrical and Electronic Engineering Plot-16, Block-B, Basundhara Dhaka 1229, Bangladesh

Abstract. The development of an effective and dependable multiple description coding scheme over a lossy communication system is described. A general framework of an effective multiple description robust communication system with two-channel and four-channel cases is presented with a proposed block-based DC coefficient relocation and AC coefficient interpolation approach. A benefit of such system is that, if all the channels work properly, a very good quality, probably lossless, reconstruction can be obtained from the received descriptions. On the other hand, if some of the channels do not work properly, a lower but still quite satisfactory quality of reconstruction can be obtained. The performance of the proposed scheme is measured with mean squared error, peak signal-to-noise ratio, entropy, and bit rate to analyze the reconstruction quality, and the computed results are matched with that of the other schemes. The system complexity is also computed and compared. Comparing the simulation results, it is observed that the proposed scheme, which uses a DC coefficient relocation and AC coefficient interpolation scheme, gives comprehensive enhancements over the other recently developed schemes. © 2013 SPIE and IS&T [DOI: 10.1117/1.JEI.22.2 .023030]

1 Introduction Reliability is one of the main concerns for wireless communication. Because of the medium uncertainty, lossless data transmission over wireless networks is not guaranteed. Packet loss in wireless communication occurs when one or more data packets fail to reach a destination. In case of sporadic packet losses, retransmission of the lost packets can be an effective solution. However, to combat bursty packet Paper 12406 received Sep. 29, 2012; revised manuscript received May 27, 2013; accepted for publication May 28, 2013; published online Jun. 21, 2013. 0091-3286/2013/$25.00 © 2013 SPIE and IS&T

Journal of Electronic Imaging

losses, multiple description coding (MDC)1–8 and reconstruction of images have received substantial consideration in the last decades due to their splendid properties over the lossy communication networks such as wireless networks, asynchronous transfer mode networks, Internet, packetswitched networks, and so on. MDC is a coding technique that fragments a single media stream into n independent subsignals ðn ≥ 2Þ referred to as descriptions.9 Descriptions can be of two types in MDC: descriptions with the same importance known as balanced MDC schemes and descriptions with different importance called unbalanced MDC schemes. After the quantization, these descriptions or subsignals are transmitted over multiple disjoint communication routes to the receiver. Applying the quantizer on the subsignals in transform domain rather than spatial domain is an advantageous idea. A transformation is, therefore, defined to map the spatial data into transformed coefficients. The transform process simply concentrates the energy into particular coefficients, generally the “lowfrequency” ones.10 Quantized transform coefficients of an image are needed to reconstruct an approximation to the original image. Different transforms will lead to different kinds of approaches in the image reconstruction. Among the different types of transform coding techniques, the JPEG image compression standard is a popular transform coding technique which uses a block-based discrete cosine transform (DCT) since DCT has excellent energy compaction for highly correlated data.11,12 The decoder, at the receiver end, reconstructs the original signal from the received subsignals by estimating the lost bitstream(s) from the received data. The benefit of this scheme is that, if all the channels work, an excellent quality, probably lossless, reconstruction is possible from all the received descriptions. However, if some of the channels are lost at

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Mansoor, Islam, and Razzak: Multiple description discrete cosine transform-based image coding. . .

the decoder, a lower but still satisfactory quality of a reconstructed image can be produced. The main idea of MDC scheme is to use a minimum redundancy in the descriptions with least complexity and with maximum data recovery from the received descriptions. Many research works have taken place recently considering these issues. Research work presented in Ref. 2 uses a multiple description scalar quantizer (MDSQ), where an index assignment scheme is used to produce two quantizers. These quantizers provide acceptable side distortion. An improved version of Ref. 2 is presented in Ref. 4, which uses wavelet transform. One of the major drawbacks of MDSQ2,4 is the design complexity of index assignment. Apparently, adjusting the redundancy is not an easy task in MDSQ. Research work presented in Ref. 8 uses a modified MDSQ, which uses two scalar quantizers on the descriptions. The scheme is less complex than that in Ref. 2 as it omits the index assignment. However, the scheme does not perform well in a low redundant system. After the DCT, pairwise correlating transform (PCT) has been performed on the descriptions in Ref. 13, where it calculates the lost coefficient from the correlated received descriptions. In this scheme, low variance coefficients are considered as zero, which limits the decoder performance at low redundancies. Another problem with PCT is that it does not have correlation among the neighboring blocks, which limits the recovery process. Research work presented in Ref. 1 uses a general MDC framework using lapped orthogonal transforms, whereas that in Ref. 1 uses an iterative procedure using maximally smooth recovery method. It has been seen that for the residual zero-mean signal, the method used in Ref. 1 fills lost coefficients with zeros. In this article, MDC for image transmission over lossy communication networks (which cannot constantly ensure lossless data transmission) has been taken under consideration. A general framework of such a diversity system with an effective and dependable MDC scheme is introduced in this constraint. As far as the image transmission is concerned, here our main focus is to perform the transmission of motionless images. At the encoder end of the proposed scheme, every 8-by-8 pixel block is transformed by type-2 DCT. For the production of the subsignals, using the interleaved splitting pattern, the resultant DCT coefficients of every block are split into two or four descriptions.1 Quantization and run-length encoding have been performed on all the subsignals. The resultant coded bitstreams from different subsignals are then transmitted through different communication routes to the receiver. The decoder first decodes the received subsignals and then the image is obtained by reconstructing the received descriptions at the decoder.

We use a conventional algebraic method to retrieve the lost DC coefficients. When some of the channels are lost, an interpolation reconstruction method is used to retrieve the lost AC coefficients. The DCT has better energy concentration with a redundancy dropping mechanism. The DCT is also easier to implement than the other transform methods. The proposed technique has the following advantages: (1) it is simple since it uses a very simple transform technique (DCT), DC coefficient relocation, and AC coefficient interpolation; (2) it is more robust against packet loss and has better reconstruction quality, especially when a fewer number of description are received at the decoder. Moreover, considering the other recently developed schemes,14–16 the proposed scheme gives very good peak signal-to-noise ratio (PSNR) values using the same bit rate and under the same loss pattern. We have also considered the execution time as a complexity measurement parameter for the proposed scheme, where we have found that the proposed scheme has less complexity and higher coding efficiency. The paper is organized as follows. In Sec. 2, the proposed MDC scheme is described after a brief review of the generation of multiple descriptions (bitstreams). Simulation results are presented in Sec. 3. Section 4 is the summary of the work. 2 Design of Proposed MDC Scheme In MDC, a frame is represented by two or more descriptions. Descriptions are passing through different channels. Compared with the original image, each description provides lower quality image. With the increasing number of received descriptions, the reconstructed image quality goes higher at the receiver end. These descriptions are independent of each other, where loss of descriptions does not hamper the reconstruction process. Figure 1 shows a general MDC framework, where the source image is divided into two descriptions. These two descriptions (descriptions 1 and 2) use channels 1 and 2, respectively. Side decoders 1 and 2 are used for descriptions 1 and 2. When one description is received, for instance, let usconsider description 1,side decoder 1 will be used, where side decoder 1 will reconstruct description 2 using the received description 1. When both the descriptions are received, the central decoder is used to reconstruct the image. 2.1 Multiple Description Production Using DC Coefficient Relocation Technique To produce multiple descriptions, a new scheme is proposed which uses block-based DC relocation and AC interpolation technique. Unlike transmitting the random coefficient blocks through the channel,1 in the proposed scheme the original signal is first decomposed into 8-by-8 blocks and then Side decoder 1

Description

Channel 1 Central decoder

Source

User

Channel 2 Description

Side decoder 2

Fig. 1 A general MDC framework for two descriptions.


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F (i, j) Original image

Description 1: B (even k or l)

DCT C (i, j) = dct2 (F (i, j))

Description 2: B (odd k or l)

Fig. 2 Block-based producing two descriptions.

transformed using DCT to generate different subsignals with unequal importance. Each subsignal or description contains the distributed coefficient blocks, where the coefficients of every 8-by-8 block is divided using interleaved splitting pattern depicted in Figs. 2 and 3. As represented in Fig. 2, for two descriptions, the first subsignal is contained with the even 8-by-8 blocks, where the DC component of the earlier block is placed at the 8, 8 position of the present block, as the DC component contains most of the energy in DCT.13–18 The second subsignal is contained with odd 8-by-8 blocks, where the DC component of the earlier block is placed at the 8, 8 position of the present block. As presented in Fig. 3, for a four-descriptions system, the first subsignal is composed of even rows-even columns of the 64-by-64 sub-block (Table 1), whereas the second and the third subsignals are composed of even rows-odd columns and odd rows-even columns, respectively. On the other hand, the fourth subsignal is composed of odd rows-odd columns of the 64-by-64 blocks with the previous block’s DC component placed in the 8, 8 position in each 8-by-8 sub-block. In Figs. 2 and 3, i and j represent the coefficient index of a block, whereas k and l represent block index. 2.2 Encoder and Decoder Pair Multiple bitstreams are obtained by splitting the input signal into multiple coded subsignals or descriptions (Figs. 2 and 3), Description 1: B (even k, even l) F (i, j) Original image

Description 2: B (even k, odd l)

DCT C (i, j) = dct2 (F (i, j))

Description 3: B (odd k, even l) Description 4: B (odd k, odd l)

Fig. 3 Production of four descriptions (i and j represent coefficient indexes, and k and l represent block indexes).

which are then transmitted over different communication routes to the receiver. Quantization and encoding on all subsignals are done by a DCT-based JPEG encoder.19–21 Quantization of the subsignals is done in the transform domain instead of the spatial domain. Two-channel and fourchannel diversity systems are considered in this article. We use a uniform quantizer for each DCT coefficient, which has a different step size for different coefficients. The run-length coding step is done by Zigzag ordering. Figure 4 shows the block diagram of the proposed MDC method for two descriptions. At the receiver end, at first the received blocks are decoded using the run-length decoding and then the blocks are dequantized. Hereafter, reconstruction of the image is done using the received descriptions at the decoder with the help of an interpolation reconstruction technique, where the lost bitstreams are predicted from the received ones. We assume that the descriptions received at the decoder are equiprobable for simplicity. For the two-channels case, side decoder 1 or side decoder 2 is used for decoding the signal when the signal of channel 1 or channel 2 is received at the receiver. The central decoder is used to decode the received signal when signals from both the channels are available (Fig. 4).

2.3 Image Reconstruction with AC Coefficient Interpolation Technique Either without recovery of lost data or with recovery of lost data, the image can be reconstructed. When all descriptions are received, an excellent quality reconstruction can be obtained. However, on the other hand, when some descriptions are not received, the matrix inversion can be done by replacing the lost coefficients with zeros. The reconstruction quality may not be that good in this case. In DCT, the DC component contains most of the energy of a particular block. So it is quite worthwhile to preserve the DC component. In the proposed algorithm, the current block is carrying the DC component of the previous block in the 8, 8 position. At the decoder, when all the descriptions are received, image reconstruction is done omitting the 8, 8 position values of any blocks. But if one or more descriptions are lost, the DC component of the lost block

Table 1 Distribution of transformed coefficients for different channels for four descriptions (the numbers in boxes indicate the coefficient block belongs to that channel).

1

2

...

...

...

...

...

...

64

1

1

2

1

2

1

2

1

...

...

2

3

4

3

4

3

4

3

...

...

.. .

1

2

1

2

1

2

1

...

...

.. .

3

4

3

4

3

4

3

...

...

.. .

1

2

1

2

1

2

1

...

...

.. .

...

...

...

...

...

...

...

...

...

64

...

...

...

...

...

...

...

...

...


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Fig. 4 Block diagram of proposed MDC method for two descriptions.

1 Cði; jÞ ¼ ½Cði − 1; jÞ þ Cði þ 1; jÞ; 2

can be retrieved from the received block. According to the proposed algorithm, the DC component of the lost block lies in the 8, 8 position of the current block. So the 8, 8 position value will be the 1, 1 position value or the DC value of the lost block. The proposed algorithm also reconstructs the AC components of the lost block by using the interpolation method. Equations used for interpolation are as follows: For two channels:

(1)

where i and j are the coefficient indexes of the 8-by-8 blocks. Considering the four-channels scenario, loss of one description, loss of two descriptions, and loss of three descriptions are the three instances that can occur. When one description is missing [Fig. 5(a)], the missing AC

C(1,1)

C(1,2)

C(1,3)

C(1,4)

C(1,5)

C(1,6)

C(1,7)

C(1,8)

C(1,1)

C(1,2)

C(1,3)

C(1,4)

C(1,5)

C(1,6)

C(1,7)

C(1,8)

C(2,1)

C(2,2)

C(2,3)

C(2,4)

C(2,5)

C(2,6)

C(2,7)

C(2,8)

C(2,1)

C(2,2)

C(2,3)

C(2,4)

C(2,5)

C(2,6)

C(2,7)

C(2,8)

C(3,1)

C(3,2)

C(3,3)

C(3,4)

C(3,5)

C(3,6)

C(3,7)

C(3,8)

C(3,1)

C(3,2)

C(3,3)

C(3,4)

C(3,5)

C(3,6)

C(3,7)

C(3,8)

C(4,1)

C(4,2)

C(4,3)

C(4,4)

C(4,5)

C(4,6)

C(4,7)

C(4,8)

C(4,1)

C(4,2)

C(4,3)

C(4,4)

C(4,5)

C(4,6)

C(4,7)

C(4,8)

C(5,1)

C(5,2)

C(5,3)

C(5,4)

C(5,5)

C(5,6)

C(5,7)

C(5,8)

C(5,1)

C(5,2)

C(5,3)

C(5,4)

C(5,5)

C(5,6)

C(5,7)

C(5,8)

C(6,1)

C(6,2)

C(6,3)

C(6,4)

C(6,5)

C(6,6)

C(6,7)

C(6,8)

C(6,1)

C(6,2)

C(6,3)

C(6,4)

C(6,5)

C(6,6)

C(6,7)

C(6,8)

C(7,1)

C(7,2)

C(7,3)

C(7,4)

C(7,5)

C(7,6)

C(7,7)

C(7,8)

C(7,1)

C(7,2)

C(7,3)

C(7,4)

C(7,5)

C(7,6)

C(7,7)

C(7,8)

C(8,1)

C(8,2)

C(8,3)

C(8,4)

C(8,5)

C(8,6)

C(8,7)

C(8,8)

C(8,1)

C(8,2)

C(8,3)

C(8,4)

C(8,5)

C(8,6)

C(8,7)

C(8,8)

(a)

(b)

C(1,1)

C(1,2)

C(1,3)

C(1,4)

C(1,5)

C(1,6)

C(1,7)

C(1,8)

C(2,1)

C(2,2)

C(2,3)

C(2,4)

C(2,5)

C(2,6)

C(2,7)

C(2,8)

C(3,1)

C(3,2)

C(3,3)

C(3,4)

C(3,5)

C(3,6)

C(3,7)

C(3,8)

C(4,1)

C(4,2)

C(4,3)

C(4,4)

C(4,5)

C(4,6)

C(4,7)

C(4,8)

C(5,1)

C(5,2)

C(5,3)

C(5,4)

C(5,5)

C(5,6)

C(5,7)

C(5,8)

C(6,1)

C(6,2)

C(6,3)

C(6,4)

C(6,5)

C(6,6)

C(6,7)

C(6,8)

C(7,1)

C(7,2)

C(7,3)

C(7,4)

C(7,5)

C(7,6)

C(7,7)

C(7,8)

C(8,1)

C(8,2)

C(8,3)

C(8,4)

C(8,5)

C(8,6)

C(8,7)

C(8,8)

(c) Fig. 5 (a) AC components interpolation of one missing block. (b) AC components interpolation of two missing blocks. (c) AC components interpolation of three missing blocks.


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Cð3; 2Þ ¼ 1∕2½Cð2; 2Þ þ Cð4; 2Þ;

coefficients are calculated by averaging the coefficients of received columns as 1 Cði; jÞ ¼ ½Cði; j − 1Þ þ Cði; j þ 1Þ; 2

(2)

where i and j are the coefficient indexes of the 8-by-8 blocks. For example, the AC coefficients calculation of a missing block Cð1; 3Þ in Fig. 5(a) is 1 Cð1; 3Þ ¼ ½Cð1; 2Þ þ Cð1; 4Þ: 2 Apparently, the AC components in the boundary are approximated by Cði; jÞ ¼ Cði; j þ 1Þ;

and i 0 s are odd: (3)

where j ¼ 1

Here i and j are the coefficient indexes of the 8-by-8 blocks. For example, the AC coefficient calculation of a boundary block Cð3; 1Þ is Cð3; 1Þ ¼ Cð3; 2Þ: In the case of two lost channels, missing coefficients are calculated by averaging the received rows [Fig. 5(b)]. For example, the AC coefficients of the missing odd rowseven columns and odd rows-odd columns are calculated by averaging the received even rows. The AC components in the boundary are approximated by Cði; jÞ ¼ Cði þ 1; jÞ;

where i ¼ 1:

(4)

Here i and j are the coefficient indexes of the 8-by-8 blocks. For example, the AC coefficient calculation of a boundary block Cð1; 2Þ in Fig. 5(b) is

2.4 Algorithm for Proposed MDC Scheme The algorithm of the proposed MDC scheme is as follows: Production of multiple description steps: Step 1: Compute 8-by-8 blocks DCT of the images. Step 2: Separate DC component of each 8-by-8 block from the AC components. Step 3: Produce multiple descriptions as follows: For two descriptions: One channel carries even rows or columns of the 8-by-8 blocks, and the other channel carries odd rows or columns of the 8-by-8 blocks. For four descriptions: Odd rows-odd columns, odd rows-even columns, even rows-odd columns, and even rows-even columns of the 8-by-8 block for the first, second, third, and fourth subsignals, respectively. Step 4: The DC component of the previous block is placed at the 8, 8 position of the current block for two or four descriptions, respectively. Encoding steps: Step 1: Generate multiple descriptions of the images by the procedure mentioned above. Step 2: Quantize each description separately by using a uniform quantizer with unequal step size depending on the frequency of the signal. Step 3: Apply an entropy-coding scheme on each subsignal separately by using a JPEG coder.

Cð1; 2Þ ¼ Cð2; 2Þ:

Decoding steps:

The other missing AC coefficients are calculated by averaging the received rows as 1 Cði; jÞ ¼ ½Cði − 1; jÞ þ Cði þ 1; jÞ: 2

Cð3; 1Þ ¼ 1∕2½Cð2; 1Þ þ Cð4; 1Þ: Consider the case where three channels are lost, which means lost AC components need to be calculated from the received data of only one channel. For example, let us consider a scenario where channels containing even roweven column data are received [Fig. 5(c)]. Using Eqs. (2) and (3), the missing odd columns’ coefficients are calculated. For example, components of Cð2; 3Þ and Cð2; 1Þ are calculated as Cð2; 1Þ ¼ Cð2; 2Þ:

Missing odd rows’ coefficients are calculated using Eqs. (4) and (5). For example, components of Cð3; 2Þ and Cð1; 2Þ are calculated as Journal of Electronic Imaging

Step 1: Decode the received subsignals separately. Step 2: Reconstruct the images depending on the descriptions received at the decoder.

(5)

For example, the AC coefficient calculation of a missing block Cð3; 1Þ in Fig. 5(b) is

Cð2; 3Þ ¼ 1∕2½Cð2; 2Þ þ Cð2; 4Þ;

Cð1; 2Þ ¼ Cð2; 2Þ:

3 Simulation Results and Discussions Using the proposed block-based DC relocation and AC interpolation approach, we have simulated a communication system. For the simulation purpose of the proposed MDC scheme, MATLAB is used. We have simulated the results for two and four descriptions (two and four connection paths between the source and destination) systems. Section 3 has been divided into two parts, Sec. 3.1 deals with the performance evaluation of the proposed method, whereas Sec. 3.2 shows the performance comparison of the proposed method with other methods. For a two-channel situation, we have compared the performance of the proposed method with different other methods (Fig. 6) for three different standard images. We have also assessed the reconstruction performance of the proposed block-based DC relocation and AC interpolation scheme with different recently developed techniques (Fig. 7) for a four-channel case.

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MD-SPIHT [14] WMDTC [15] WDIR [16] Proposed

Fig. 6 Comparison of PSNR values for the reconstructed image with one available channel in a two-channel case at 0.5 bpp.

3.1 Performance Evaluation To depict the performance evaluation of the proposed method, we have considered different configurations of the proposed system. Image reconstruction without the AC and DC components recovery, image reconstruction with only DC component recovery, and image reconstruction with both DC and AC components recovery are the three different configurations that have been considered (Fig. 8) in a fourchannel environment. From Fig. 8, it is found that when all the channels work well, all the configurations yield same output images. Reconstructing the DC component of the lost description gives better quality image than that without recovery configuration. Again, if both the AC and the DC components are recovered, excellence has been found in the output image for any loss combination. For the recovery of the DC component, the relocation method has been proposed in this paper, whereas for the recovery of the AC components, we are using the interpolation method. Performance analysis in terms of PSNR, mean squared error (MSE), bit rate, and entropy of the proposed MDC scheme for the two-channel scenario are presented in Fig. 9(a) and 9(b). Here, standard image Lena has been considered for the analysis. In the proposed scheme, PSNR values are 27.62, 27.57, and 36.59 dB with the availability of channel 1, channel 2, and both channels, respectively [Fig. 9(a)]. Channel 1 gives an MSE (gray level) of 112.45 and channel 2 gives 113.92, whereas the MSE (gray level) goes down to 14.24 when both the channels are available

[Figure 9(a)]. Channel 1 gives a bit rate of 0.28 bpp and channel 2 gives 0.29 bpp, whereas the bit rate goes to 0.45 bpp when both the channels are available [Fig. 9(b)]. Entropy values are 0.87, 0.87, and 0.90 bpp with the availability of channel 1, channel 2, and both channels, respectively [Fig. 9(b)]. Analyzing the simulation results in Fig. 9(a) and 9(b), we can see that no matter how many descriptions are received, our proposed scheme can guarantee a satisfactory reconstruction quality. Performance analysis in terms of PSNR, MSE, bit rate, and entropy of the proposed MDC scheme for the four-channel scenario are presented in Fig. 10(a) and 10(b). PSNR values are 26.10, 27.67, 30.06, and 36.60 dB with the availability of one channel, two channels, three channels, and all four channels, respectively, for the proposed scheme [Fig. 10(a)]. When one channel is available or one description is received, the MSE (gray level) is 159.58, availability of two channels gives an MSE of 111.25, and availability of three channels gives an MSE (gray level) of 64.12, where the MSE value goes down to 14.25 when all four channels are available [Fig. 10(a)]. When one channel is available or one description is received, the bit rate is 0.20 bpp, availability of two channels gives 0.42 bpp, and availability of three channels gives 0.61 bpp, whereas the bit rate goes up to 0.81 bpp when all four channels are available [Fig. 10(b)]. Entropy values are 0.83, 0.87, 0.89, and 0.90 bpp with the availability of one channel, two channels, three channels, and all four channels, respectively [Fig. 10(b)]. Analyzing the simulation results in Fig. 10(a) and 10(b), we can see that no matter how many descriptions are received, our proposed scheme can guarantee a satisfactory reconstruction quality. 3.2 Performance Comparison To evaluate the performance of the proposed method, we have compared the simulation results with other recently developed methods. With the availability of one description for a two-channel case, we have analyzed the reconstruction quality of the proposed relocation method with other methods (Fig. 6). Three different standard test images (Lena, Baboon, and Barbara) are considered to check the reconstruction performance at same bit rate (0.5 bpp). For the test image Lena, the PSNR values of the reconstructed

LOT-based maximally smooth recovery [1]

Wavelet domain interpolation for tree reconstruction method [16] Proposed method

Fig. 7 Performance comparison of the proposed method with other methods (in terms of PSNR for the four-channel case).


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Fig. 8 Reconstructed images for four-channel case: (a) original image, (b) without recovery of AC and DC components, (c) DC component reconstruction with relocation method, and (d) proposed interpolation method with DC and AC components reconstruction, where the first row shows reconstructed images when all four channels are available, second row shows reconstructed images when three channels are available, third row shows reconstructed images when two channels are available, and fourth row shows reconstructed images when one channel is available.

(a)

(b)

Fig. 9 (a) PSNR and MSE of the proposed method for the two-channel case. (b) Bit rate and entropy of the proposed method for the two-channel case.

images are 17.02, 21.99, 25.05, and 27.62 dB in multiple description-set partitioning in hierarchical trees (MDSPIHT) method,14 multiple descriptions transform coding algorithm based on wavelet (WMDTC) method,15 wavelet domain interpolation for tree reconstruction (WDIR) method,16 and the proposed method, respectively. In the Journal of Electronic Imaging

case of the test image Baboon, the PSNR values of the reconstructed images are 17.10, 22.05, 25.18, and 27.01 dB in MD-SPIHT method, WMDTC method, WDIR method, and the proposed method, respectively. Considering the test image Barbara, the PSNR values of the reconstructed images are 16.07, 21.65, 24.41, and 26.68 dB in the

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Fig. 10 (a) PSNR and MSE of the proposed method for the four-channel case. (b) Bit rate and entropy of the proposed method for the fourchannel case.

MD-SPIHT method, WMDTC method, WDIR method, and the proposed method, respectively. In all the cases, it has been found that the proposed method gives better reconstruction quality than others (Fig. 6). Simulation results of the proposed block-based DC coefficients relocation and AC coefficients interpolation method are compared with different reconstruction schemes for the standard image Lena in Fig. 7. With the same bit rate and under the same loss pattern, we are considering the values of PSNR as the performance evaluating factor for different methods in Fig. 7. When all descriptions are available, the values of PSNR for lapped orthogonal transform (LOT)based maximum smooth recovery method, wavelet domain interpolation for tree reconstruction method, and the proposed method are 34.99, 36.12, and 36.59 dB, respectively. If three descriptions are available, PSNR values for LOTbased maximum smooth recovery method, wavelet domain interpolation for tree reconstruction method, and the proposed method are 26.29, 27.67, and 30.06 dB, respectively. In the case of two available descriptions, the values of PSNR for LOT-based maximum smooth recovery method, wavelet domain interpolation for tree reconstruction method, and the proposed method are 22.87, 25.12, and 27.67 dB, respectively. When one description is available, the PSNRs are 18.62 dB in LOT-based nonhierarchical signal decomposition with maximally smooth recovery technique and 22.19 dB in wavelet domain interpolation for tree reconstruction method, whereas the PSNR goes up to 26.10 dB using the proposed MDC scheme. PSNR values of the proposed block-based DC relocation and AC interpolation method are higher compared with the other methods for

all cases (Fig. 7). When all descriptions are available, that is, when all four descriptions are available, all the methods present similar PSNR values. But when some descriptions are lost, the proposed method gives better PSNR values, which means the reconstructed image qualities are higher in the proposed block-based DC relocation and AC interpolation method. The proposed method also reduces the blocking effect significantly than any other methods because of the preservation and better reconstruction of DC components in each 8-by-8 blocks. The reconstruction quality of the experimental image Lena (512 × 512, 8 bpp) in terms of received descriptions in a two-channel scenario is depicted in Fig. 11 and that in a four-channel scenario is presented in Fig. 12. From Figs. 11 and 12, it can be stated that the quality of the reconstructed image goes higher with the increasing number of descriptions received at the decoder. The quality of the reconstructed images for a four-channel system using different MDC schemes is presented in Fig. 12. It is found that when all channels are working properly, all the MDC schemes’ performances are virtually the same, i.e., the quality of the reconstructed images for all methods yield nearly the same performance. But in the case of losing subsignals or descriptions, the proposed block-based DC relocation and AC interpolation scheme provides a better reconstruction performance compared to the other MDC schemes. Finally, the simulation results of the proposed blockbased DC relocation and AC interpolation scheme are matched with different MDC approaches. Here the execution time is taken as the complexity measurement parameter. In

Fig. 11 Reconstructed images for the two-channel case: (a) original image, (b) reconstructed images when both the channels are available, (c) reconstructed images when one channel is available.


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Fig. 12 Reconstructed images for the four-channel case: (a) original image, (b) LOT-based smooth recovery method, (c) wavelet domain interpolation for tree reconstruction method, and (d) proposed block-based DC relocation and AC interpolation method, where first row represents reconstructed images when all four channels are available, second row represents reconstructed images when three channels are available, third row represents reconstructed images when two channels are available, and fourth row represents reconstructed images when one channel is available.

the simulation environment, execution time of the proposed MDC for a two-channel system is 3.6231 s, whereas the execution time is 4.7190 s for the DC separation method.6 The proposed method uses fewer mathematical operations compared to the other methods used for the reconstruction purpose, which makes the proposed scheme computationally faster. For all the cases, the simulation environment remains the same. Since the proposed method does not use any extra redundancy, it is less complex than other recently developed methods. 4 Conclusion In this article, we have presented a newly developed framework of MDC scheme to accomplish multiple description image transmission for two-channel and four-channel systems. In this proposed approach, the encoder first decomposes the input signal using the proposed block-based DC relocation and AC interpolation method to produce the Journal of Electronic Imaging

descriptions and then encodes all subsignals or descriptions individually. At the receiver end, the decoder is used to process the received descriptions in each channel to produce the decoded subsignal. After that, the reconstruction of the image is done from the received descriptions. The quality of the image reconstruction visibly depends on the number of descriptions received at the decoder. Considering the twochannel system, PSNR values are 27.62, 27.57, and 36.59 dB with the availability of channel 1, channel 2, and both channels, respectively, whereas in the four-channel system, PSNR values are 26.10, 27.67, 30.06, and 36.60 dB with the availability of one channel, two channels, three channels, and all four channels, respectively. From the PSNR values, we can say that when all the channels work properly, the proposed scheme can reconstruct a very good quality image. Again, in the case of losing subsignals or descriptions, the proposed scheme can reconstruct a satisfactory quality image, which is better than those reconstructed by other schemes.

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Acknowledgments This research is partially supported by Malaysia Japan International Institute of Technology Research Grant with Vote No. 4J044 and GUP TIER 2 with Vote No. 08J77 of Ministry of Higher Education for the year 2012 to 2013. We thank the reviewers of JEI for the comments that greatly improved the manuscript. References 1. C. Doo-Man and W. Yao, “Multiple description image coding using signal decomposition and reconstruction based on lapped orthogonal transforms,” IEEE Trans. CAS 9(6), 895–908 (1999). 2. V. A. Vaishampayan, “Design of multiple description scalar quantizers,” IEEE Trans. Inf. Theory 39(3), 821–834 (1993). 3. M. Srinivasan and R. Chellappa, “Multiple description subband coding,” in Proc. IEEE Intl. Conf. Image Processing, Part 1, Vol. 1, pp. 684–688 (1998). 4. S. D. Servetto et al., “Multiple-description wavelet based image coding,” in Proc. Intl. Conf. Image Processing, Part 1, Vol. 1, pp. 659–663 (1998). 5. J. C. Batllo and V. Vaishampayan, “Asymptotic performance of multiple description transform codes,” IEEE Trans. Inf. Theory 43(2), 703–707 (1997). 6. G. Sun et al., “Multiple description coding with prediction compensation,” IEEE Trans. Image Process. 18(5), 1037–1047 (2009). 7. T. Tillo, M. Grangetto, and G. Olmo, “Multiple description image coding based on Lagrangian rate allocation,” IEEE Trans. Image Process. 16(3), 673–683 (2007). 8. M. A. Razzak et al., “Multiple description image transmission for diversity systems over unreliable communication networks,” in 10th Int. Conf. Computer and Information Technology, pp. 68–71, United International University, Bangladesh (2007). 9. V. K. Goyal, “Multiple description coding: compression meets the network,” IEEE Signal Process. Mag. 18(5), 74–93 (2001). 10. P. Dragotti, S. Servetto, and M. Vetterli, “Optimal filter banks for multiple description coding: analysis and synthesis,” IEEE Trans. Inf. Theory 48(7), 2036–2052 (2002). 11. A. K. Jain, Fundamentals of Digital Image Processing, 3rd reprint, Prentice Hall (2004). 12. S. Li et al., “Recovering missing coefficients in DCT-transformed images,” in 18th IEEE Int. Conf. Image Processing, pp. 1537–1540 (2011). 13. Y. Wang et al., “Multiple description coding using pairwise correlating transforms,” IEEE Trans. Image Process. 10(3), 351–366 (2001). 14. A. C. Miguel, A. E. Mohr, and E. A. Riskin, “SPIHT for generalized multiple description coding,” in Int. Conf. Image Processing, Vol. 1, pp. 842–846 (1999). 15. J. Liu and Y. Yu, “Research on multiple descriptions transform coding algorithm based on wavelet,” J. Comput. Appl. 25(2), 317–319 (2005). 16. Y. Shi et al., “A novel multiple-description image coding on wavelet,” in 10th Pacific Rim Conf. Multimedia, pp. 1257–1262 (2009). 17. S. Li et al., “An improved DC recovery method from AC coefficients of DCT-transformed images,” in 17th IEEE Int. Conf. Image Processing, pp. 2085–2088 (2010). 18. K. Veeraswamy and S. S. Kumar, “Adaptive AC-coefficient prediction for image compression and blind watermarking,” J. Multimed. 3(1), 16–22 (2008). 19. G. K. Wallace, “The JPEG still-picture compression standard,” ACM Commun. J. 34(4), 30–44 (1991). 20. W. B. Pennebaker and J. L. Mitchell, JPEG Still Image Data Compression Standard, Van Nostrand Reinhold, New York (1992). 21. Z. Xiong et al., “A comparative study of DCT- and wavelet-based image coding,” in IEEE Trans. Circ. Syst. Video Technol. 9(5), 692–695 (1999).


Nafees Mansoor received his BSc degree in computer science from the Independent University, Bangladesh (IUB) in 2005 and his MSc degree in telecommunication engineering from IUB in 2008. Currently he is doing his PhD in electrical engineering at Malaysia-Japan International Institute of Technology (MJIIT), Universiti Teknologi Malaysia (UTM), Malaysia. He was recognized as cum laude in his BSc degree. Recently, he has received the award for the Best Research Proposal in the JACTIM Research Proposal Contest, 2012. His research interests cover image coding, cognitive radio networks, and wireless communication protocols. A. K. M. Muzahidul Islam received his MSc in computer science and engineering from Kharkiv National University of Radio Electronics, Ukraine, in 1999 and his DEng in computer science and engineering from Nagoya Institute of Technology, Japan, in 2007. He has received the Japanese Government Monbusho Scholarship (October 2002 to March 2006). He has worked in various industries in Bangladesh and Japan. Currently, he is working as a senior lecturer at MJIIT of UTM. His current research interests include algorithm, image processing, wireless sensor network, communication protocol, network security, cloud computing, and cognitive radio network. M. Abdur Razzak received his MEng and PhD in electrical engineering from Nagoya University, Japan, in 2003 and 2006, respectively. Currently, he is working as an associate professor in the Department of Electrical & Electronic Engineering of IUB, Bangladesh. He has received a number of academic awards, including University Gold Medal (1995), Japanese Government Scholarship (2000), IEEE Scholar Award (2005), Hori Information Promotion Award (2005), and Japan Society for Promotion of Science (JSPS) Postdoctoral Fellowship (2008). His research interests include facial expression recognition, image coding, and cloud computing. He has published more than 96 research papers in peer-reviewed journals, and international and domestic conference proceedings. He has been invited as a keynote speaker in a number of international conferences. He is the organizing chair of the International Conference on Advances in Electrical Engineering held biennially in Dhaka, Bangladesh. He is also serving as the reviewer of half a dozen peer-reviewed journals and international conferences. He is serving as an editorial board member of the Recent Patents of Signal Processing.

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