Chapter 5, Image Restoration Video Solutions, Digital Image Processing

Problem 1

A signal with power spectral density
$$
|X(k)|^2=\{64,0,0,0,0,0,0,0\}
$$
has been blurred by a process with finite impulse response
$$
\left\{h_d(0)=0.5, h_d(1)=0.5\right\}
$$
and corrupted by an additive Gaussian noise with power spectral density
$$
\{0.0002,0.0071,0.0273,0.0121,0.0220,0.0121,0.0273,0.0071\}
$$
The samples of the degraded signal are
$$
y(n)=\{0.9898,0.9759,1.0319,1.0313,0.9135,0.9970,0.9835,1.0628\}
$$
Restore the true signal using the Wiener filter.

James Kiss

Numerade Educator

Problem 2

A signal with power spectral density
$$
|X(k)|^2=\{0,16,0,0,0,0,0,16\}
$$
has been blurred by a process with finite impulse response
$$
\left\{h_d(0)=0.5, h_d(1)=0.5\right\}
$$
and corrupted by an additive Gaussian noise with power spectral density
$$
\{0.0119,0.0058,0.0807,0.0107,0.1725,0.0107,0.0807,0.0058\}
$$
The samples of the degraded signal are
$$
y(n)=\{-0.4305,0.3907,0.8310,0.9653,0.2446,-0.3503,-0.7983,-0.7435\}
$$
Restore the true signal using the Wiener filter.

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Problem 3

A signal with power spectral density
$$
|X(k)|^2=\{0,0,16,0,0,0,16,0\}
$$
has been blurred by a process with finite impulse response
$$
\left\{h_d(0)=0.5, h_d(1)=0.5\right\}
$$
and corrupted by an additive Gaussian noise with power spectral density
$$
\{0.0067,0.1671,0.1262,0.1311,0.1654,0.1311,0.1262,0.1671\}
$$
The samples of the degraded signal are
$$
y(n)=\{0.6544,0.5086,-0.6492,-0.5742,0.3938,0.7350,-0.5616,-0.4252\}
$$
Restore the true signal using the Wiener filter.

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Problem 4

A signal with power spectral density
$$
|X(k)|^2=\{0,0,0,16,0,16,0,0\}
$$
has been blurred by a process with finite impulse response
$$
\left\{h_d(0)=0.5, h_d(1)=0.5\right\}
$$
and corrupted by an additive Gaussian noise with power spectral density
$$
\{0.0772,0.0694,0.0930,0.0001,0.0545,0.0001,0.0930,0.0694\}
$$
The samples of the degraded signal are
$$
y(n)=\{0.1272,0.2353,-0.4300,0.2133,-0.2887,-0.0976,0.3358,-0.3732\}
$$
Restore the true signal using the Wiener filter.

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Problem 5

A signal with power spectral density
$$
|X(k)|^2=\{0,0,16,0,0,0,16,0\}
$$
has been blurred by a process with finite impulse response
$$
\left\{h_d(0)=0.5, h_d(1)=0.5\right\}
$$
and corrupted by an additive Gaussian noise with power spectral density
$$
\{0.1584,0.0055,0.0030,0.1719,0.0047,0.1719,0.0030,0.0055\}
$$
The samples of the degraded signal are
$$
y(n)=\{-0.3581,0.5292,0.5198,-0.3412,-0.5804,0.5697,0.5835,-0.5244\}
$$
Restore the true signal using the Wiener filter.

Check back soon!