feat(v5): add periodic noise and fft reconstruction

backend/processing/registry.py

@@ -192,6 +192,29 @@ def average_noisy_copies(image, params):
     return ensure_uint8(np.round(total / count))
 
 
+def periodic_noise(image, params):
+    """Add sinusoidal periodic noise controlled by amplitude A and period T.
+
+    Use it to reproduce lecture examples where repeating row/column patterns create visible frequency spikes.
+    """
+
+    amplitude = float(params.get("A", 0.2))
+    period = float(params.get("T", 100))
+    if not np.isfinite(amplitude) or not np.isfinite(period) or period <= 0:
+        raise ProcessingError("A must be finite and T must be a finite positive number.")
+
+    height, width = image.shape[:2]
+    y = np.arange(height, dtype=np.float32)[:, None]
+    x = np.arange(width, dtype=np.float32)[None, :]
+    mask = amplitude * np.sin(2.0 * math.pi * y / period) + amplitude * np.sin(2.0 * math.pi * x / period)
+
+    source = image.astype(np.float32) / 255.0
+    if image.ndim == 3:
+        mask = mask[:, :, None]
+    noisy = np.clip(source + mask, 0.0, 1.0)
+    return ensure_uint8(np.round(noisy * 255.0))
+
+
 def gaussian_filter(image, params):
     """Apply a Gaussian low-pass filter controlled by mask size K and variance Q.
 
@@ -347,6 +370,24 @@ def fft_spectrum(image, params):
     return gray_to_rgb(normalize_to_uint8(magnitude))
 
 
+def inverse_fft_reconstruction(image, params):
+    """Reconstruct an image with real(ifft2(ifftshift(fftshift(fft2(image))))).
+
+    Use it to demonstrate that FFT followed by inverse FFT recovers the image when no filter is applied.
+    """
+
+    def reconstruct_channel(channel):
+        source = channel.astype(np.float32)
+        spectrum = np.fft.fftshift(np.fft.fft2(source))
+        reconstructed = np.real(np.fft.ifft2(np.fft.ifftshift(spectrum)))
+        return np.round(np.clip(reconstructed, 0, 255)).astype(np.uint8)
+
+    if image.ndim == 2:
+        return reconstruct_channel(image)
+    channels = [reconstruct_channel(image[:, :, idx]) for idx in range(image.shape[2])]
+    return np.stack(channels, axis=2)
+
+
 def operation(id, label, chapter, slide_group, func, params=None, supports="both", matrices=None, formula="", repeatable=True):
     """Create one operation registry entry consumed by the API and frontend."""
 
@@ -385,6 +426,10 @@ OPERATIONS = [
         "mean": float_param(0, -1, 1, 0.01, description="Gaussian mean in normalized intensity units."),
         "variance": float_param(0.01, 0, 0.2, 0.005, description="Gaussian variance; lower values add weaker noise."),
     }, formula="result = (1/N) sum_i (f + n_i), with gaussian n_i.", repeatable=False),
+    operation("periodic_noise", "Periodic Noise", CH3, "Noise and Denoising", periodic_noise, {
+        "A": float_param(0.2, 0, 1, 0.01, description="Amplitude A of the sinusoidal noise in normalized intensity units."),
+        "T": float_param(100, 1, 512, 1, description="Period T of the horizontal and vertical sinusoidal noise in pixels."),
+    }, formula="g(x,y) = f(x,y) + A sin(2*pi*y/T) + A sin(2*pi*x/T)."),
     operation("box_filter", "Average / Box Filter", CH3, "Linear Low-Pass Filters", box_denoise, {"K": odd_param(3, 35, description="Odd mask dimension K for the K x K average mask.")}, matrices=[kernel_preview("1 / K^2 box mask", [["1", "1", "1"], ["1", "1", "1"], ["1", "1", "1"]], "1 / K^2")], formula="g = imfilter(f, ones(K,K)/K^2)"),
     operation("weighted_average", "Weighted Average Filter", CH3, "Linear Low-Pass Filters", weighted_denoise, matrices=[kernel_preview("Weighted average mask", [[1, 2, 1], [2, 4, 2], [1, 2, 1]], "1 / 16")], formula="g = imfilter(f, weighted mask)"),
     operation("gaussian_filter", "Gaussian Filter", CH3, "Linear Low-Pass Filters", gaussian_denoise, {"K": odd_param(3, 35, description="Odd Gaussian mask dimension K."), "Q": float_param(1.0, 0.01, 25, 0.1, description="Variance Q of the Gaussian mask.")}, formula="Gaussian mask controlled by K and variance Q."),
@@ -401,6 +446,7 @@ OPERATIONS = [
     ], formula="Gradient image = abs(imfilter(f,Gx)) + abs(imfilter(f,Gy))."),
     operation("high_boost", "High-Boost / Edge Emphasis", CH3, "High-Boost Filtering", high_boost_slide, {"A": float_param(1.5, 1, 6, 0.1, description="Boost factor A, where A >= 1."), "K": odd_param(3, 35, description="Odd averaging mask size used for the blurred image.")}, formula="f_hb = A f - blurred(f)."),
     operation("fft_spectrum", "FFT/DFT Spectrum View", CH4, "DFT and FFT", fft_spectrum, {"mode": select_param("log_magnitude", ["magnitude", "log_magnitude", "phase"], description="Choose magnitude, log magnitude, or phase display.")}, formula="F(u,v) = DFT{f(x,y)}", repeatable=False),
+    operation("inverse_fft_reconstruction", "Inverse FFT Reconstruction", CH4, "DFT and FFT", inverse_fft_reconstruction, formula="f = real(ifft2(ifftshift(fftshift(fft2(image))))).", repeatable=False),
     operation("rgb_to_gray", "Convert to Grayscale", CH6, "Color Conversion", rgb_to_gray_matlab, {"red_weight": float_param(0.299, 0, 1, 0.001, description="R coefficient in gray = aR + bG + cB."), "green_weight": float_param(0.587, 0, 1, 0.001, description="G coefficient in gray = aR + bG + cB."), "blue_weight": float_param(0.114, 0, 1, 0.001, description="B coefficient in gray = aR + bG + cB.")}, formula="gray = 0.299R + 0.587G + 0.114B by default.", repeatable=False),
     operation("rgb_channel", "RGB Channel View", CH6, "RGB color model", rgb_channel, {"channel": select_param("r", ["r", "g", "b"], description="Select the RGB channel to view.")}, formula="Show one RGB channel as grayscale.", repeatable=False),
 ]