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3.9 Exercises 179

Figure 3.66 There is a faint image of a rainbow visible in the right hand side of this picture. Can you think of a
way to enhance it (Exercise 3.29)?

2. Fit an additive rainbow function (explain why it is additive) to this arc (it is best to work
with linearized pixel values), using the spectrum as the cross section, and estimating
the width of the arc and the amount of color being added. This is the trickiest part of
the problem, as you need to tease apart the (low-frequency) rainbow pattern and the
natural image hiding behind it.

3. Amplify the rainbow signal and add it back into the image, re-applying the gamma
function if necessary to produce the final image.

Ex 3.30: Image deblocking—challenging Now that you have some good techniques to
distinguish signal from noise, develop a technique to remove the blocking artifacts that occur
with JPEG at high compression settings (Section 2.3.3). Your technique can be as simple
as looking for unexpected edges along block boundaries, to looking at the quantization step
as a projection of a convex region of the transform coefficient space onto the corresponding
quantized values.
1. Does the knowledge of the compression factor, which is available in the JPEG header
information, help you perform better deblocking?
2. Because the quantization occurs in the DCT transformed YCbCr space (2.115), it may
be preferable to perform the analysis in this space. On the other hand, image priors
make more sense in an RGB space (or do they?). Decide how you will approach this
dichotomy and discuss your choice.

3. While you are at it, since the YCbCr conversion is followed by a chrominance subsam-
pling stage (before the DCT), see if you can restore some of the lost high-frequency
chrominance signal using one of the better restoration techniques discussed in this
chapter.

4. If your camera has a RAW + JPEG mode, how close can you come to the noise-free
true pixel values? (This suggestion may not be that useful, since cameras generally use
reasonably high quality settings for their RAW + JPEG models.)