1. A Novel Method for Burst Error Recovery of Images First Author: S. Talebi Second Author: F. Marvasti Affiliations: King’s College London E-mail: farokh.marvasti@kcl.ac.uk

2. I. The Proposed Technique II. Simulation III. Noise Sensitivity IV. Conclusion V. Future Work

3. I. The Proposed Technique We use a new transform such that the kernel of the transform is equal to where q 1 and q 2 are positive prime integers with respect to N. It can be shown that this kernel is a sorted kernel of DFT.

4. The polynomial error locator is (1) (2) The inner summation is the SDFT of the missing samples e(i m,k n ), hence (3)

5. The remaining values of E(r,d) can be found from (4) by the following recursion (4) The SDFT is actually derived from DFT and the fast algorithm can still be used. Because the SDFT transform can be handled by DFT and sorting; the sorting of the elements is as follows for m,n =1,..,N that a SDFT is the element of the SDFT transform matrix and a DFT is the element of the DFT transform matrix.

6. Figure 1. The zeros are inserted around the original matrix X org (m,n) to get the X over (m,n) ( “  ” are the padded zeros and “ * “ are the elements of the X org (m,n) )

7. II. Simulation A (256  256) image is used for the simulation of the algorithm. A number of zeros are inserted in the rows and columns of the SDFT matrix and a new matrix of size of (512  512) is derived. The Mean Squared Error for this simulation is equal to 1.09  10 -15.

9. III. Noise Sensitivity III(a)- Quantization Noise: For our proposed method, the sensitivity of the algorithm is simulated as follows. The over-sampled image is quantized to 8 bits before the transmission. The corresponding SNRs before the transmission and after reconstruction of this simulation are equal to 38.2 dB and 35.02 dB, respectively.

10. III(b) Additive Noise A white random noise of uniform distribution is added to the quantize transmitted image (SNR=28.6dB). The SNR after the recovery of the original image is equal to 28.193dB. The result for this case is shown in the next Fig. The SNR values show that the new method is robust against additive and quantization noise. This can be attributed to the low dynamic range of the coefficients h t,f,which results in small amount of accumulated round off error in the solution of the difference equation (4).

12. IV. Conclusion –We have shown that the new algorithm has three advantages: –1- It is ideal to recover the missing pixels for large blocks of bursty errors. –2- In terms of complexity, it is simpler than other techniques. –3- It is very robust in correcting bursts of errors with respect to additive and quantization noise. –Disadvantage of this method is that the ratio between the recovery pixels and the added zeros is 1/3.

13. V. Future Work –Application of this method in the case of compressed image will be consider next. –The extension of the method to recover randomly distributed pixel losses is currently under investigation.