Given a 4 ×4 image, compute the entropy. Find the Huffman...

Given a $4 \times 4$ image, compute the entropy. Find the Huffman code representation of its unique symbols and the bpp. (i) $$ \left[\begin{array}{rrrr} 144 & 113 & 121 & 107 \\ 144 & 110 & 121 & 103 \\ 129 & 109 & 120 & 99 \\ 116 & 108 & 121 & 103 \end{array}\right] $$ (ii) $$ \left[\begin{array}{llll} 209 & 190 & 179 & 179 \\ 143 & 136 & 132 & 129 \\ 131 & 130 & 125 & 117 \\ 113 & 109 & 118 & 143 \end{array}\right] $$ (iii)

Given a $4 \times 4$ image, compute the entropy. Find the Huffman code representation of its unique symbols and the bpp.
(i)
$$
\left[\begin{array}{rrrr}
144 & 113 & 121 & 107 \\
144 & 110 & 121 & 103 \\
129 & 109 & 120 & 99 \\
116 & 108 & 121 & 103
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{llll}
209 & 190 & 179 & 179 \\
143 & 136 & 132 & 129 \\
131 & 130 & 125 & 117 \\
113 & 109 & 118 & 143
\end{array}\right]
$$
(iii)

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Key Concepts

Entropy

Entropy is a measure from information theory that quantifies the uncertainty or randomness in a set of symbols based on their probabilities. It represents the average information content per symbol and is used to determine the theoretical lower bound on the number of bits needed to encode data without loss.

Probability Distribution

A probability distribution describes the likelihood of occurrence of each unique symbol in the dataset. In the context of images, it refers to how frequently each pixel value appears, which is essential for calculating the entropy and creating efficient coding schemes.

Huffman Coding

Huffman coding is a lossless data compression algorithm that assigns variable-length codes to symbols based on their frequencies, with shorter codes for more frequent symbols. This method ensures that the average code length is minimized, making it an optimal prefix code strategy for encoding data.

Bits per Pixel (bpp)

Bits per pixel is a metric used in image processing to indicate the number of bits used to represent each pixel in an image. When using compression techniques like Huffman coding, bpp corresponds to the average number of bits required per pixel based on the optimally encoded symbols.

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