Chapter 13, Image Compression Video Solutions, Digital Image Processing

Problem 1

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)

Check back soon!

04:06

Problem 2

Given a $4 \times 4$ image, decompose it into 4 bit planes and represent each of them by run-length coding. Use both the methods.
(i)
$$
\left[\begin{array}{rrrr}
6 & 6 & 15 & 14 \\
8 & 8 & 4 & 11 \\
9 & 9 & 10 & 12 \\
10 & 14 & 13 & 1
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{rrrr}
11 & 9 & 15 & 14 \\
13 & 7 & 6 & 7 \\
6 & 5 & 5 & 5 \\
11 & 4 & 4 & 2
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{rrrr}
13 & 9 & 12 & 10 \\
13 & 13 & 12 & 9 \\
13 & 13 & 12 & 9 \\
11 & 13 & 12 & 10
\end{array}\right]
$$

Emily Min

Numerade Educator

Problem 3

Given a $4 \times 4$ image, find the linear predictive code. Find the entropies of the input and the code.
(i)
$$
\left[\begin{array}{llll}
15 & 16 & 20 & 20 \\
15 & 15 & 19 & 22 \\
15 & 16 & 19 & 20 \\
15 & 17 & 19 & 16
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{lllll}
158 & 157 & 154 & 149 \\
168 & 153 & 157 & 149 \\
170 & 152 & 157 & 149 \\
166 & 153 & 157 & 142
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{rrrr}
106 & 103 & 98 & 99 \\
121 & 122 & 108 & 93 \\
102 & 102 & 100 & 99 \\
100 & 101 & 102 & 96
\end{array}\right]
$$

Check back soon!

01:48

Problem 4

Given a 1-digit sequence, find its arithmetic code. Reconstruct the sequence from the code. Let there be three symbols $\{1,2,3\}$ and number of occurrences of the symbols, respectively, be $\{2,1,1\}$ in a sequence of length 4 .
(i) $\{1\}$
(ii) $\{2\}$

Varsha Aggarwal

Numerade Educator

Problem 5

Given a sequence $x(n)$, find the 1-level DWT coefficients using the $9 / 7$ filter. Assume whole-point symmetry at the borders. Verify that the reconstructed signal is the same as the input.
(i)
$$
\{1,-4,1,3,3,1,3,0,2,2,3,1,-5,2,0,3\}
$$
(ii)
$$
\{1,2,1,1,3,4,0,3,1,3,2,-1,0,1,4,-3\}
$$
(iii)
$$
\{-2,0,2,-2,1,0,3,1,-2,1,2,-1,2,0,-2,1\}
$$

Check back soon!

Problem 6

Given a $4 \times 4$ image, find its compressed version using the 1-level Haar DWT and the Huffman code. What is the bpp and SNR.
(i)
$$
\left[\begin{array}{lllll}
170 & 168 & 164 & 173 \\
179 & 167 & 167 & 167 \\
184 & 179 & 173 & 166 \\
183 & 179 & 184 & 173
\end{array}\right]
$$
(ii)
$$
\left[\begin{array}{lllll}
172 & 173 & 170 & 171 \\
171 & 176 & 173 & 172 \\
174 & 178 & 172 & 170 \\
176 & 175 & 171 & 170
\end{array}\right]
$$
(iii)
$$
\left[\begin{array}{llll}
162 & 163 & 163 & 161 \\
162 & 164 & 161 & 161 \\
163 & 165 & 164 & 162 \\
167 & 161 & 162 & 164
\end{array}\right]
$$

Check back soon!