Consider the simple 4 × 8, 8-bit image:212121951692432432432121219516924324324321212195169...

Consider the simple 4 × 8, 8-bit image:

(a) Compute the entropy of the image.

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(b) Compress the image using Huffman coding.

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(c) Compute the compression achieved and the effectiveness of the Huffman coding.

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(d) Consider Huffman encoding pairs of pixels rather than individual pixels. That is, consider the image to be produced by the second extension of the zero-memory source that produced the original image. What is the entropy of the image when looked at as pairs of pixels?

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(e) Consider coding the differences between adjacent pixels. What is the entropy of the new difference image? What does this tell us about compressing the image?

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(f) Explain the entropy differences in (a), (d) and (e).