An image uses 512 × 512 picture elements. Each of the picture elements can take any of the 8 distinguishable intensity levels. The maximum entropy in the above image will be A. 2097152 bits B. 786432 bits C. 648 bits D. 144 bits

The correct answer is A. 2097152 bits.

The maximum entropy of an image is the entropy of the image with the most uniform distribution of probabilities. In this case, each of the 512 × 512 picture elements can take any of the 8 distinguishable intensity levels, so the probability of each intensity level is 1/8. The entropy of this image is then $H = -\sum_{i=1}^8 p_i \log p_i = -\frac{8}{8} \log \frac{8}{8} = 8 \log 8 = 2097152$ bits.

Option B is incorrect because it is the entropy of an image with a uniform distribution of probabilities, but the image in the question does not have a uniform distribution of probabilities.

Option C is incorrect because it is the entropy of an image with a non-uniform distribution of probabilities, but the image in the question does not have a non-uniform distribution of probabilities.

Option D is incorrect because it is the entropy of an image with a uniform distribution of probabilities, but the image in the question does not have a uniform distribution of probabilities.