Purpose:

Write pseudocode to introduce noise into an image and then apply convolution to reconstruct the original image by reducing or eliminating the noise.

Requirements:

Part $1$: Introduce Noise

a$.$ Write pseudocode to add random noise to a given image. The noise can be "salt and pepper" noise, where random pixels are set to either the minimum or maximum intensity, or Gaussian noise, where random values from a normal distribution are added to pixel intensities.

b$.$ Hint for Noise Introduction:

i$.$ Salt and Pepper Noise: Loop through each pixel in the image. For each pixel, with a small probability, set its value to either the minimum or maximum intensity.

ii$.$ Gaussian Noise: For each pixel, add a random value sampled from a Gaussian distribution $($with a defined mean and standard deviation$)$ to the pixel's intensity.

Part $2$: Apply Convolution for Image Reconstruction

a$.$ Write pseudocode to apply a convolution filter $($such as a Gaussian blur or median filter$)$ that will help reduce the noise and attempt to reconstruct the original image.

b$.$ Hint for Convolution:

i$.$ Define a convolution kernel $($e$.$g$.,$ a Gaussian or median kernel$).$

ii$.$ Slide the kernel across the image, computing the new pixel values based on neighboring pixels to smooth or average out the noise.

iii. Set padding: Decide on padding $($e$.$g$.,$ zero$-$padding or edge$-$padding$)$ to handle edges of the image. Padding ensures the kernel can cover all pixels, even those at the edges.

iv$.$ Set slide parameters: Determine the stride or step size for sliding the kernel across the image. A stride of $1$ means moving one pixel at a time, while a larger stride skips pixels for faster, but potentially less precise, convolution.

v$.$ Slide the kernel across the image, compute new pixel values based on neighboring pixels to smooth or average out the noise.