2016/2/171 Image Vector Quantization Indices Recovery Using Lagrange Interpolation Source: IEEE International Conf. on Multimedia and Expo. Toronto, Canada, 2006 Author : Yung - Gi Wu and Chia - Hao Wu Student : Pei - Jun Jiang R Advisor : W. J. Chen

2016/2/172 Outline ► ► Introduction ► ► The proposed scheme ► ► Simulation results ► ► Conclusion

2016/2/173 Introduction ► ► Vector Quantization   Developed by Gersho and Gray in 1980   Some other coding devised ► ► Discrete cosine transform, block truncation coding, wavelets coding, etc.   One of the most successful signal processing techniques ► ► Quick and simple on decoding   Encode ► ► Cut the image apart into the matrix of M *N ► ► Get a codebook, which each code vector has codewords ► ► Searches a best match code-vector in the codebook ► ► The best match code-vector have replaced the vector ► ► Transmit the code-vector index to the channel

2016/2/174 Introduction   Decode ► ► Using these received indices to get code-vectors form the codebook ► ► Reconstruct the decoded image ► ► Internet transmission   The indices may be lost ► ► Random noises ► ► Re-transmitting the data   Wastes of time ► ► Estimate these lost data and to recover them   Much more fast then re-transmitting the data   Large data lost may cause the receiver determine the network disconnection

2016/2/175 Introduction ► ► Lagrange Interpolating Polynomial   The first published by Waring in 1779   Rediscovered by Euler in 1783   Published by Lagrange in 1795   The polynomial P(x) of degree < or = (n-1) that passes through the n points (x 1,y 1 =f(x 1 )), (x 2,y 2 =f(x 2 )),..., (x n,y n =f(x n )),

2016/2/176 Introduction given by where Written explicitly

2016/2/177 Introduction ► ► The main ideal of the proposed method   Decreasing the network traffic capacity   Maintaining the network traffic capacity quality as well as possible   Will not be considered when the data is lost seriously ► ► Causes network disconnection

2016/2/178 Outline ► ► Introduction ► ► The proposed scheme ► ► Simulation results ► ► Conclusion

2016/2/179 The proposed scheme ► ► Using Lagrange interpolation formula ► ► Two parts   Preprocessing process   Recovery process Fig 1 System diagram

2016/2/1710 The proposed scheme ► Preprocessing process  Sort codebook ► Increase the relationship between near vectors of codebook  Classify the code-vectors in the codebook as follow:  Only sort the codebook once ► Before any other process ► Off-line Fig 2 Preprocessing process diagram D i : difference V : code-vectors i : i-th ε: threshold

2016/2/1711 The proposed scheme ► Recovery process  Lagrange interpolation  Uses the correct indices  Set the lost index M,and L1, L2, R2, R1 are the correct indices ► Use L1, L2, R2, R1 to estimate and recover the lost M yiyi L1L1 L2L2 MR2R2 R1R1 xixi Fig 3 Recovery process diagram Table 1 Polynomial corresponding coordinates for each index

2016/2/1712 The proposed scheme ► ► Two-way polynomial   Horizontal and vertical   Different four coefficients for each way yiyi L1L1 L2L2 MR2R2 R1R1 horizontal[m-1,n-1][m,n-1][m,n][m,n+1][m+1,n+1] vertical[m-1,n+1][m,n+1][m,n][m,n-1][m+1,n-1] Table 2 Coordinates of coefficient L2L2 L1L1 MR1R1 R2R2 R2R2 R1R1 M L1L1 L2L2 Horizontal Vertical

2016/2/1713 Outline ► ► Introduction ► ► The proposed scheme ► ► Simulation results ► ► Conclusion

2016/2/1714 Simulation results ► ► Test image : Lenna,size is 512×512 codebook size is 256 threshold ε = 128 ► ► Random recovery   Recovery those lose indices by random padding ► ► Low-pass filter   Eliminate the random noise

2016/2/1715 Simulation results VQ indices lost-rate(%) Non recovery Random recovery Low-pass filter One-way Lagrange Two-way Lagrange Table 3 The quality of reconstructed image (Lenna) expressed in dB with different methods and different lost -rates

2016/2/1716 Simulation results ► In high data lost-rate  Two-way Lagrange is powerful than other methods ► In low data lost-rate  Two-way Lagrange is not so obvious Figure 4 The quality of reconstructed image (Lenna) with different methods and different lost-rates

2016/2/1717 Simulation results Figure 5 Original Lenna image Figure 6 The VQ reconstructed image (PSNR = 30.15dB) Figure 7 Lost-rate 1%Figure 8 Random indices recovery at lost-rate 1% PSNR = dB Figure 9 Low-pass filter recovery at lost-rate 1% PSNR =29.607dB Figure 10 Two-way Lagrange recovery at lost-rate 1% PSNR=29.735dB Figure 11 Lost-rate 5%Figure 12 Random indices recovery at lost-rate 5% PSNR = dB Figure 13 Low-pass filter recovery at lost-rate 5% PSNR =27.331dB Figure 14 Two-way Lagrange at lost-rate5% PSNR=28.418dB

2016/2/1718 Simulation results One hundred 512 X 512 gray level images Using two-way Lagrange to recovery Retransmission (T1 network :1.544Mbps) 31 milliseconds8290seconds Bit rate = 0.5 ► Recover one image is about 0.31 milliseconds ► Using two-way Lagrange to recovery  Could be used in time requirement application Table 4 Compare the waste time of recovery images and retransmission images

2016/2/1719 Outline ► ► Introduction ► ► The proposed scheme ► ► Simulation results ► ► Conclusion

2016/2/1720 Conclusion ► ► An efficient data recovery method for VQ encoded image transmission ► ► If the data lost happens   Do not request to transmit these data again ► ► Wastes of time   Using the received correct data ► ► Estimate and recover the lost data ► ► Efficient in time-constraint situation ► ► Using Lagrange interpolating polynomial ► ► Property   Fast processing   The reconstructed images have visual acceptable quality

2016/2/1721 Thanks~