Problem 1 equation below [2] Parametric Wiener Filter (a) Implement a motion blu

Question

Problem 1 equation below

[2] Parametric Wiener Filter (a) Implement a motion blurring filter as in proble (b) Blur image 5.26(a) in the +45o direction using T 1, as in Fig. 5.26(b) (ab0. (c) Add a small amount of Gaussian noise of 0 mean to the blurred image. For this, you can use the Matlab command: mnoise(I,'gaussian',0,v) adds Gaussian white noise of mean 0 and variance v to the image I (the parameter v needs to be specified). The default is zero mean noise with 0.01 variance. (d) Restore the image using the parametric Wiener filter given by 1 H(u, )2 u, v)2+ G(u,v), where K is a specified constant, chosen to obtain best visual results. note that you may have to avoid division by zero in the above formula)

Explanation / Answer

Note: The code is implemented in Matlab

To create a blurring filter below are the steps.

Image= imread('Image name'); ///Please provide the image name

imshow(Image);

b. 2. We will be using a motion filter to blur the image and then displaying the blurred image.

Note: We are blurring image in the 45 degree direction using T=1

H = fspecial('motion',20,45);

MotionBlurred = imfilter(Image,H,'replicate');

imshow(MotionBlurred); //Displaying the blurred image

c. Adding a small amount of Gaussian noise of 0 mean to blurred image

gaussiannoiseimage=imnoise(MotionBlurred,'gaussian'); //adds zero-mean, Gaussian white noise with variance of 0.01 to grayscale image MotionBlurred.

imshow(gaussiannoiseimage); ///displaying the blurred image with gaussian noise

Note: We ccan also add other types of noises as shown below

J = imnoise(I,'gaussian') adds zero-mean, Gaussian white noise with variance of 0.01 to grayscale image I.

J = imnoise(I,'gaussian',m) adds Gaussian white noise with mean m and variance of 0.01.

J = imnoise(I,'gaussian',m,var_gauss) adds Gaussian white noise with mean m and variance var_gauss.

J = imnoise(I,'localvar',var_local) adds zero-mean, Gaussian white noise of local variance var_local.

J = imnoise(I,'localvar',intensity_map,var_local) adds zero-mean, Gaussian white noise. The local variance of the noise, var_local, is a function of the image intensity values in I. The mapping of image intensity value to noise variance is specified by the vector intensity_map.

J = imnoise(I,'poisson') generates Poisson noise from the data instead of adding artificial noise to the data. See Algorithms for more information.

J = imnoise(I,'salt & pepper') adds salt and pepper noise, with default noise density 0.05. This affects approximately 5% of pixels.

example

J = imnoise(I,'salt & pepper',d) adds salt and pepper noise, where d is the noise density. This affects approximately d*numel(I) pixels.

J = imnoise(I,'speckle') adds multiplicative noise using the equation J = I+n*I, where n is uniformly distributed random noise with mean 0 and variance 0.04.

J = imnoise(I,'speckle',var_speckle) adds multiplicative noise with variance var_speckle.

gpuarrayJ = imnoise(gpuarrayI,___) adds noise to the gpuArray intensity image gpuarrayI, performing the operation on a GPU. This syntax requires the Parallel Computing Toolbox™.

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