1. A Novel Error Correction Method without Overhead for Corrupted JPEG Images M. Bingabr and P.K. Varshney Syracuse University ICIP 2002

2. Outline Introduction Detection And Correction Algorithm for An Image Block Experimental Results

3. Introduction JPEG overview AC DCT Quantization DPCM RLC VLC 8x8 A C Zigzag DC AC iDCT

4. Introduction If the DCT coefficients C kt and C pq are corrupted, the whole image will be corrupted. A r : reconstructed A. C e : error amplitude of C.

5. Detection and Correction Algorithm for An Image Block A e xy : error amplitude of A. Select three reference pixels A uc, A vc, and A wc in the same column c of A. 1 2 3 Selection of three reference pixels: ★ Selected by the encoder and then send to receiver with no loss. ★ Selected by average of all neighboring pels. ★ Selected with a fixed pixel value. e.g. 128.

6. Detection and Correction Algorithm for An Image Block From and From and k, p  [0, 7]. There are 28 possible combinations of k and p. 12 4 5 43

7. Detection and Correction Algorithm for An Image Block Choose a suitable (u, v, w) will get 28 distinct α values satisfying. u=2, v=4, w=7 5

8. Detection and Correction Algorithm for An Image Block Scenarios –Two errors occur in two rows There is exactly one (k, p) fulfilling. –Two errors occur in the same row (k = p) There are seven α fulfilling, but they all have the same row or column. –Errors occur in more than two rows The algorithm fails. 5 5

9. Detection and Correction Algorithm for An Image Block After getting k and p, use the same approach to get t and q from the other three reference pixels A ru, A rv, A rw. C e kt and C e pq can be obtained from A xy = A r xy – A e xy ★ t errors in a block can be corrected by 2t+1 reference pixels.

10. Experimental Results 512 x 512 Tank Two-state Markov channel model Rcv-img: no error correction. RS: received image when RS(63,59) channel coding and interleaving with depth 128 is applied to the transmitted DCT coefficients. BVWO: proposed algorithm with depth 128 interleaving. BVwO nc : proposed algorithm without error concealment.

11. Experimental Results Time and computational complexity