Can the deconvolution Wiener filter reduce noise without having a blurred image?

Question

I am trying to denoise many several noises with several filters for a research i have, i found a deconvolution Wiener filter made by "mr.tranleanh" on Github, as you can see here .

what I did is that I canceled the blurring part in the code and only add Gaussian noise to my images, and I made a PSNR calculation each time I apply the filter, and for each time I was increasing the size of the Gaussian kernel the PSNR value is getting bigger, so that's mean that the noise is being reduced, and all that without adding blurring to the image.

I am wondering whether I can use the Wiener filter for reducing noise in this way (without blurring).

• Can a deconvolution Wiener filter reduce noise without blurring?
• Why does the image get darker each time I apply the Wiener filter?

Shortly this is how I wrote the code:

def add_gaussian_noise(img, sigma):
    gauss = np.random.normal(0, sigma, np.shape(img))
    noisy_img = img + gauss
    noisy_img[noisy_img < 0] = 0
    noisy_img[noisy_img > 255] = 255
    return noisy_img
def wiener_filter(img, kernel, K):
    kernel /= np.sum(kernel)
    dummy = np.copy(img)
    dummy = fft2(dummy)
    kernel = fft2(kernel, s = img.shape)
    kernel = np.conj(kernel) / (np.abs(kernel) ** 2 + K)
    dummy = dummy * kernel
    dummy = np.abs(ifft2(dummy))
    return dummy
def gaussian_kernel(kernel_size = 3):
    h = gaussian(kernel_size, kernel_size / 3).reshape(kernel_size, 1)
    h = np.dot(h, h.transpose())
    h /= np.sum(h)
    return h
def rgb2gray(rgb):
    return np.dot(rgb[...,:3], [0.2989, 0.5870, 0.1140])
if __name__ == '__main__':
    # Load image and convert it to gray scale
    file_name = os.path.join('/content/Hand.jpeg') 
    img = rgb2gray(plt.imread(file_name))
    # Add Gaussian noise
    noisy_img = add_gaussian_noise(blurred_img, sigma = 20)
    # Apply Wiener Filter
    kernel = gaussian_kernel(3)
    filtered_img = wiener_filter(noisy_img, kernel, K = 10)

edited :

the type of images I want to apply the wiener filter on :

they are just normal gray images, but I will add salt&pepper noise by this code :

   import cv2

  def add_noise(img):

row , col = img.shape
number_of_pixels = random.randint(300, 10000 )
for i in range(number_of_pixels):
    y_coord=random.randint(0, row - 1)
    
    x_coord=random.randint(0, col - 1)
    
    img[y_coord][x_coord] = 255
    
number_of_pixels = random.randint(300 , 10000)
for i in range(number_of_pixels):

    y_coord=random.randint(0, row - 1)
    x_coord=random.randint(0, col - 1)
    img[y_coord][x_coord] = 0
return img
img = cv2.imread('/content/Hand.jpeg',
                cv2.IMREAD_GRAYSCALE)
cv2.imwrite('s&p12spe.jpg', add_noise(img))

the full code for adding salt&pepper noise source in case you want more explanation.

again I just want to denoise salt&pepper noise via Wiener filter, and I know salt&pepper noise is denoised via other filters like median filter, but am doing this for research purposes, and the only code I found for the Wiener filter is the one I uploaded here in the question, i don't know if more information can help you, but thanks anyway

Answer 1

For Salt and Pepper noise on medical or real world images using the Wiener Filter isn't recommended.

The Wiener filter basically takes advantage only on the knowledge from the spectrum of the data.
The spectrum is global while the data of those kind of images is very local: Edges, Contrast, Texture, etc...

Hence a much better approach would be using local filters.
You may try the 2D Median filter which is a classic solution for the Salt and Pepper noise model. You may also use the Bilateral Filter with some tweaking for this kind of noise.

Basically, any Edge Preserving Filter will do much better preserving the details while suppressing noise.

Answer 2

Can a deconvolution Wiener filter reduce noise without blurring?

Maybe. Maybe not. There is not one Wiener filter. Any concrete "Wiener filter" is a plain old filter that has been designed using the algorithm for defining a filter laid out by Norbert Weiner, and given exact descriptions of the underlying signal's spectrum, and the noise.

You can, within limitations, choose the filter you want, then choose noise and signal characteristics that will result in that filter. If you want a high-pass filter (or at least a high frequency boost filter), choose a signal with no DC content, and white noise. You'll get an edge-enhance filter. If you want a low-pass filter, choose a signal with little high frequency content, and white noise. You'll get a filter that blurs. If you want some random filter, choose your signal and your noise randomly.

Why does the image get darker each time I apply the Wiener filter?

Because when you randomly chose a signal characteristic that's almost white, and white noise, the result is a filter that attenuates everything.

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What you are missing in your design process is this: Weiner filters are only optimal if the noise is Gaussian and stationary and known, and if the signal acts as if it were generated by a known linear system excited by Gaussian white noise, and if the optimality criterion is mean-squared error.

In image processing, the signal statistics are almost never act like they were generated by a linear system excited by Gaussian white noise, the optimality criterion is almost never mean-squared error (although sometimes it's better to pretend so). In the case of salt-and-pepper noise, the signal statistics are most definitely not Gaussian, although they may act like they're generated by some stationary process.

So the choice of a Wiener filter to enhance an arbitrary image that's beset by salt-and-pepper noise does not check any of the boxes for using a Wiener filter.

In fact, most of the check boxes for any linear filter at all remain empty when you're looking at salt-and-pepper noise. And, indeed, the filter that ends up getting used most often -- the median filter -- is not a linear filter, and it works pretty well.