A Simple Image Compression : JPEG

1. A Simple Image Compression : JPEG Overall Process : • The image is broken into 8x8 blocks of pixels • Working from Left to Right and Top to Bottom, Discrete Cosine Transform(DCT) is applied to each of the 8x8 blocks. • Each Block is compressed through Quantization • The array of compressed blocks that constitute the image is stored in a drastically reduced amount of space. • The image is reconstructed by the use if Inverse Discrete Cosine Transform(IDCT).

2. DCT Computation The DCT Coefficient D(i,j) for the (i,j) pixel is computed as follows:

3. DCT Computation For a standard (8x8) block as used in jpeg, N=8 and (x,y) range from 0 to 7. Hence, the DCT computation has reduced to:

4. Matrix Representation of the DCT Equation Let Tij be computed as :

5. Matrix form of Tij For an (8x8) block, it results in the matrix:

6. DCT Computation on an (8x8) Block

7. DCT Computation

8. DCT Computation

9. DCT Computation

10. Quantization

11. Quantization

12. Quantization Levels

13. Quantization Levels

14. Quantization

15. Quantization Zeros represent less important higher frequencies that can be discarded.

16. Coding

17. Decompression

18. Inverse DCT and Decompression

19. Comparison

20. Finally ….

21. Further Levels