feat(v5): add periodic noise and fft reconstruction

README.md

@@ -73,6 +73,7 @@ The app is organized as a small MATLAB-like image workspace. Each operation crea
 - **Bit-plane slicing** displays one binary bit of each gray value. Formula: `bit_k(r)`.
 - **Noise filter** adds test noise. Gaussian noise uses `g = f + n`; salt-and-pepper noise randomly sets pixels to `0` or `255`.
 - **Average N noisy copies** generates `N` independent Gaussian-noisy copies of the current image and averages them into one result. Formula: `result = (1/N) * sum_i(f + n_i)`.
+- **Periodic noise** adds a repeating sinusoidal row and column pattern. Formula: `g(x,y) = f(x,y) + A sin(2*pi*y/T) + A sin(2*pi*x/T)`.
 - **Average / box filter** smooths an image with a uniform mask. Formula: `g = imfilter(f, ones(K,K) / K^2)`.
 - **Weighted average filter** smooths with the slide mask `1/16 * [[1,2,1],[2,4,2],[1,2,1]]`.
 - **Gaussian filter** smooths using a Gaussian mask controlled by size `K` and variance `Q`. Formula: `G(x,y) = exp(-(x^2+y^2)/(2Q))`.
@@ -85,7 +86,8 @@ The app is organized as a small MATLAB-like image workspace. Each operation crea
 
 ### Chapter 4: Frequency Domain
 
-- **FFT/DFT spectrum view** shows magnitude, log magnitude, or phase of the image in the frequency domain. Formula: `F(u,v) = DFT{f(x,y)}`.
+- **FFT/DFT spectrum view** shows magnitude, log magnitude, or phase of the image in the frequency domain. Formula: `F(u,v) = DFT{f(x,y)}`. Apply it to a periodic-noisy state with `log_magnitude` to see the noise peaks.
+- **Inverse FFT reconstruction** applies FFT then inverse FFT without filtering to demonstrate reconstruction. Formula: `f = real(ifft2(ifftshift(fftshift(fft2(image)))))`.
 
 ### Chapter 6: RGB Color Processing