Periodic Noise
- Periodic noise is a type of spatially dependent noise that typically arises from electrical or electromechanical interference during image acquisition.
- It is usually represented as sinusoidal patterns added to the image.
Characteristics:
- Appears as repeating patterns in the image (e.g., ripples, waves).
- It is the only spatially dependent noise discussed in this chapter.
- In the frequency domain, periodic noise appears as pairs of conjugate impulses.
Removal Technique:
- We can use frequency domain filtering to reduce or eliminate periodic noise by:
- Detecting spikes in the Fourier spectrum.
- Removing the corresponding frequency components.
Example:
- In Fig. 5.5(a): An image corrupted with sinusoidal noise.
- In Fig. 5.5(b): The Fourier transform shows two spikes corresponding to the noise frequency.
Removing these spikes helps clean the image.
2. Estimating Noise Parameters
To perform image restoration, it is essential to estimate the parameters of noise—either from the sensor or the image itself.
A. Frequency Domain Estimation (For Periodic Noise):
- Analyze the Fourier spectrum of the noisy image.
- Look for visible spikes (frequency components of the interference).
- Estimate noise periodicity and strength by inspecting the location and size of these spikes.
B. Spatial Domain Estimation (For PDF-based Noise):
- Used when the PDF model of the noise (Gaussian, Rayleigh, Uniform, etc.) is assumed.
✅ Two common methods:
i. Using “Flat” Images (Sensor Access Available)
- Capture uniformly lit, gray images using the imaging device.
- These “flat field” images reflect the true system noise.
- Calculate:
- Mean (μ) and variance (σ²) of pixel intensities.
ii. Using Sample Patches (Sensor Not Available)
- Select a small subimage (S) with uniform background intensity.
- Calculate histogram and estimate:
- Probability values for intensity levels.
- Mean and variance using formulas:
Formulas:
- Match the shape of the histogram to known PDFs (Gaussian, Rayleigh, etc.)
- For salt-and-pepper noise, estimate the probability of salt (white) and pepper (black) pixels by measuring the peak heights of the histogram at 0 and 255 (for 8-bit images).