Bildkompression mit SVD

src/FHGR_CDS_Nume_E_PYNU_SVD_Bildkompression.py

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+# Python
+# AUEM
+# 2026-05-06
+# Begin
+# --------------------------------------------------------------------------------------
+# Python initialisieren:
+from PIL import Image, ImageOps
+import matplotlib.pyplot as pl
+import numpy as np
+
+# Parameter:
+N = 10
+sc_r = 100
+pr = 3
+fig = 1
+# Import:
+img = Image.open("./Bild.JPG")
+img_sw = ImageOps.grayscale(img)
+A = np.asarray(img_sw)
+# Berechnungen;
+[U, S, Vt] = np.linalg.svd(A)
+U_red = U[:, :N]
+S_red = S[:N]
+Vt_red = Vt[:N, :]
+A_red = U_red @ np.diag(S_red) @ Vt_red
+G = A.size
+G_red = U_red.size + S_red.size + Vt_red.size
+r = G_red / G
+# Anzeige der Bilder:
+fh = pl.figure(fig)
+pl.imshow(A, cmap="gray")
+fig = fig + 1
+fh = pl.figure(fig)
+pl.imshow(A_red, cmap="gray")
+# Ausgabe:
+print("--------------------------------------------------")
+print(__file__)
+print("--------------------------------------------------")
+print(f"Groesse original:        G = {G}")
+print(f"Groesse komprimiert: G_red = {G_red}")
+print(f"Datenkompression:        r = {r*sc_r:#.{pr}g}%")
+print("--------------------------------------------------")
+# --------------------------------------------------------------------------------------
+# End