Lab 6

Lab 6#

Denoising#

This exercise is intended to evaluate the performances of the denoising method of your choice. Therefore it is essential to have an image corrupted by noise and the same image without noise to be able to compare the denoising method with the actual image.

Creation of a noisy image#

  • Recall the mathematical definition of SNR.

  • Express the power of the noise in terms of SNR.

  • In the case of an AWGN, the power of the noise is a good estimation of the variance of the Gaussian. Express the Gaussian variance \(\sigma^2\) in terms of SNR.

  • Add noise to the image of your choice by using skimage.util.random_noise (with parameter clip=False to get a real Gaussian noise).

    Note

    • Use a grayscale image (skimage.color.rgb2gray).

    • For convenience, it is recommended to use an image of size less than 1000×1000. Use skimage.transform.rescale to reduce the image size.

    • Be careful to work with floats. You may need to convert your image with .astype(float).

  • Check that the noise level corresponds to the expected SNR. For example, noise should be barely visible above 30 dB. On the contrary, the image should be difficult to discern below 0 dB.

Denoising the noisy image#

Now that you dispose of a noisy image and its noiseless version, you can implement the denoising method.

  • Denoise the image with the chosen method:

    • If you choose a mean filter, use scipy.ndimage.convolve to filter by a square PSF h = np.ones((w,w)) / (w*w) of size w.

    • If you choose TV regularization, use skimage.restoration.denoise_tv_chambolle.

  • Observe visually the effect of the parameter (size of the mean filter or regularization parameter) on the result, especially for extreme values.

  • Use skimage.metrics.mean_squared_error to calculate the mean squared error (MSE, in French EQM for erreur quadratique moyenne) of the denoised image to have a quantitative measure of the denoising quality.

  • Represent the evolution of the MSE according to the parameter, and comment on the result: what is the optimal value of this parameter? Can you adjust the parameter by knowing the SNR of the image?

  • Compare your method with the one implemented by another student.

Deconvolution#

  • Load the image 5.1.13. It will be called \(x\) in the sequel.

  • Generate a circular PSF \(h\) of radius 10 with skimage.morphology.disk.

  • Perform the convolution of \(x\) by \(h\) to obtain the image \(y\). To do this, use the function scipy.ndimage.convolve with the argument mode="wrap" so that the convolution is circular.

  • Apply the inverse filter on \(y\) to get an estimate \(\widehat{x} \) of \(x\). What do you see?

  • Add a small noise to the blurred image, then apply the inverse filter again. What do you see?

  • Now replace the inverse filter with Wiener filter (skimage.restoration.wiener with argument clip=False).

  • Study the influence of the regularization parameter: first by observing the result obtained for some values, then by representing the evolution of a restoration quality measure (which one?) with respect to the values of the regularization parameter.

  • What is the optimal value of the regularization parameter? Do you agree that it is actually the best value when you look at the estimation?

  • Finally, can you conclude on the optimal choice of the regularization parameter, whatever the image?

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