python(denoising): Image denoising

Signed-off-by: prescientmoon <git@moonythm.dev>

python/denoising/flake.nix

@@ -9,7 +9,7 @@
       (system:
         let
           pkgs = nixpkgs.legacyPackages.${system};
-          pyDeps = p: with p; [ numpy scipy matplotlib ];
+          pyDeps = p: with p; [ numpy scipy matplotlib pillow ];
         in
         rec {
           devShell = pkgs.mkShell {

python/denoising/modules/image_tools.py

@@ -0,0 +1,46 @@
+"""Project 2 tools for generating a noisy image"""
+import matplotlib.pyplot as plt
+import numpy as np
+from PIL import Image  # PIL is an image processing module
+
+
+def create_noisy_image(path="/content/drive/My Drive/", file="sonic.jpg"):
+    """Transform color image to a noisy grayscale image.
+    Plot and save the transformed images.
+
+    The file sonic.jpg must be located in your google drive and the drive must have been
+    "mounted" with:
+
+        from google.colab import drive
+        drive.mount("/content/drive")
+    """
+    image = Image.open(path + file)
+    # Transform RGB image to grayscale
+    image = image.convert("L")
+
+    # get the filename without the extension
+    # (note: the pathlib module offers better ways to do this!)
+    name = file.removesuffix(".jpg")
+
+    image.save(path + name + "_gray.jpg")
+
+    # set images to be plotted in gray scale
+    plt.gray()
+    plt.imshow(image)
+    plt.title("Original image")
+    plt.show()
+
+    # add noise to grayscale image
+    sigma = 2.0
+    img_arr = np.array(image)
+    img_arr_noisy = np.clip(
+        img_arr + sigma * np.random.normal(0, 100, img_arr.shape), 0, 255
+    ).astype(np.uint8)
+    plt.title("Noisy image")
+    plt.imshow(img_arr_noisy)
+
+    # create Image object from numpy array and save to disk
+    image = Image.fromarray(img_arr_noisy, mode="L")
+    image.save(path + name + "_gray_noisy.jpg")
+
+    plt.show()

python/denoising/modules/tridiagonal.py

@@ -43,23 +43,7 @@ def to_csr(a, c, e):
   """
   assert_valid_tridiagonal(a, c, e)
 
-  n = len(c)
-
-  values = np.zeros(n * 3 + 1)
-  values[::3] = a
-  values[1::3] = c
-  values[2::3] = e
-  
-  col_indices = np.zeros_like(values)
-  col_indices[1::3] = np.arange(1, n + 1)
-  col_indices[2::3] = np.arange(0, n)
-  col_indices[3::3] = np.arange(1, n + 1)
-
-  index_ptr = np.zeros(n + 2)
-  index_ptr[1:n+1] = np.arange(2, n * 3 + 2, 3)
-  index_ptr[n+1] = n * 3 + 1
-
-  return sp.sparse.csr_array((values, col_indices, index_ptr))
+  return sp.sparse.diags((a, c, e), offsets=(0, 1, -1), format="csr")
 
 def to_array(a, c, e):
   """
@@ -230,6 +214,12 @@ def scale(s, m):
 
   return result
 
+def transpose(a, c, e):
+  """
+  Computes the transpose of a tridiagonal matrix.
+  """
+  return create(a, e, c)
+
 # Small sanity check for the above code
 def main():
   a, c, e = create(3*np.ones(4), 2*np.ones(3), 3*np.ones(3))