## WAVELET-BASED IMAGE COMPRESSION## Conclusions and Forward-Thinking Statements |

Considering our goal was to come up with a way to compress an image using wavelets, I'd say we reached our goal. We succeeded in representing an image using symmetric, biorthogonal wavelets, applied some sort of thresholding to the wavelet representation, and took the inverse. We subjectively compared the results from our compression algorithm to explore the tradoffs between including more bases in the compressed image, and the compression ratio.

Ways that we could have improved upon our work included:

- Determining a better quantization scheme
- Comparing soft thresholding to our own thresholding technique
- Calculating the resulting energy in the compressed image to quantify the success of a set of parameters for compression

Overall, however, I'd say we did a good job of meeting our project objectives.

The JPEG-2000 standard is based on the discrete wavelet transform using the Daubechies(9,7) biorthogonal wavelet. Moreover, the JPEG-2000 standard also uses novel ways of scalar quantization, context modeling, arithmetic coding and post-compression rate allocation. The steps involved in compression using the JPEG-2000 standard are the same as those used in our baby example of using the DWT to compress an image, only it seems that the JPEG-2000 standard uses a different set of basis functions, and there's alot of research going on into ROI (region of interest) coding, since the assumption is that these JPEGs are going to go across lossy channels, and when determining the quality of the image that comes out on the other side, one is most interested in just a part of the image, the ROI.

We can't say that what we did is anywhere near the level of the work that is being done on the JPEG-2000 standard, but we did succeed in representing a quantized image using a set of wavelet basis functions, and applying some sort of thresholding to 'compress' the image.