A lossless compression with low complexity transform
5. Rice-Golomb Coding
The special case of Golomb codes with m=2
kchoosing m to be a power of 2 leads to very simple
encoding/decoding procedures: the code for n
³ 0 consists of the k least significant bits of n, followed by
the formed number by the remaining higher order bits of n, in binary representation. The length of the
encoding is k+1+[ n/2
k]
Fig 6. The example of Rice-Golomb coding
In order to find k for Golomb coding, the encoder and decoder maintain two variables per context: N, a
count of prediction residuals seen so far, and A, the accumulated sum of magnitudes of prediction
residuals. The coding parameter k can be computed by
Results
Figure7 shows the two different continuous tone images, were transformed to DCT coefficient and
remapped. The first image is flatter than the second one. The corresponding transformed coefficients are
shown in same way. To increase the continuous of coefficients can be done by remapping procedure as
shown in Figure (b) and (c).
Table 1 Lossless compres sion comparision
For the high continuous tone image, the compressed image sizes seem not difference in three method
and evidently observe when compared with the low continuous tone image.
Conclusion
The proposed method has taken the advantages of both transform and context based compressions.
The DCT transform can reduce the interpixel redundancy, while context based Rice-Golomb coding
offers the high reduction of coding redundancy. This proposed method shows the performances as high
as continuous level that will degrade the compression ratio when applies with the previous method
(Weinberger, 1996) or JPEG-baseline.
References
- Weinberger, M. J., 1996. LOCO-I: A low complexity, context-based, lossless image compression
algorithm, pp.140-149.
- Gonzales, R. C., 1993. Digital Image Processing, Wesley Publishing Company.
- Golumb, S. W., 1966. Run-length encodings, Vol. IT-12, pp.399-401.
- Rice, R. F., 1979. Some practical universal noiseless coding techniques. In: Jet Propulsion Laboratory,
Pasadena, CA, U.S.A., Rep. JPL-79-22.
