Summary and Conclusions
Image compression using transform coding yields extremely good compression, with controllable degradation of image quality. By adjusting the quantization of the transform coefficients, a compromise can be made between image quality and compression factor. In general, the quality of the compressed image is inversely proportional to the compression ratio, and very high compression is achieved with acceptable image quality.

A DCT based image coder and a wavelet based image coder were implemented in this project, however the main focus was the DCT based coder. Consequently, most of the optimization effort was spent on the latter, and superior results were achieved. Although the Wavelet based coder produced good visual image quality, with higher computational efficiency, the quantization portion of this implementation should be improved to enhance image quality. The superior computational efficiency of the wavelet transform suggests that it is more suitable than the DCT for real-time applications, where image coding must be performed in real-time. An example of such an application is the digital still-camera, which typically requires image coding and storage before a subsequent photograph can be taken. A long delay time between photographs is usually not acceptable.

The quality of the compressed representation was assessed by visual comparison to the original image, as well as by calculation of mean squared error (MSE). As we improved the quantization scheme to reduce MSE, the perceived image quality actually decreased. Initially, our implementation divided the DCT coefficients by the magnitude of the largest coefficient. The coefficients were then multiplied by 127, to achieve full 8-bit resolution during quantization. This approach yielded very high visual quality, but poor MSE. To correct this, we scaled each coefficient by dividing by our maximum quantization value. This scheme ensures that each value can be represented by an 8-bit signed integer (i.e. range -127 to 127), however it only uses the full dynamic range when the DCT contains coefficients with the maximum and minimum magnitudes possible (+/-1024). As expected, this approach produced inferior, perceived image quality, but a considerable MSE improvement was achieved.

Another example where the mean squared error proved to be a poor measure of visual image quality was seen in the results for the wavelet based coder. The wavelet based coder yielded a higher MSE than the DCT based coder, however in almost all cases the resulting image looked smoother (mostly due to the blocking effect of the DCT based scheme). These observations suggests that the MSE is not a good metric for image quality, and other metrics should be employed.





Back..