Stripe Noise Removal in Images Using Fourier Transform with Multiple Filtering Approaches

Fourier transform-based stripe noise removal represents a fundamental technique in digital image processing. The Fourier transform converts images from the spatial domain to the frequency domain, enabling noise filtration through frequency-domain manipulation. In implementation, we typically apply the 2D Fast Fourier Transform (FFT) to decompose the image into its frequency components, where stripe noise manifests as distinct high-frequency patterns along specific orientations.

Three primary filtering strategies are employed in this approach. The Ideal Low-Pass Filter completely attenuates frequencies beyond a specified cutoff radius while preserving all frequencies within it - implemented computationally by creating a binary mask that zeros out high-frequency components outside the cutoff circle. The Butterworth Low-Pass Filter provides a smoother transition between passed and suppressed frequencies, controlled by an order parameter that determines the steepness of the cutoff slope; this avoids the ringing artifacts commonly associated with ideal filters. The Gaussian Low-Pass Filter utilizes a Gaussian function to gradually attenuate high-frequency components, with the standard deviation parameter controlling the filter's bandwidth and smoothing characteristics.

Each filter requires specific parameter tuning: cutoff frequency for ideal filtering, cutoff frequency and order for Butterworth, and sigma value for Gaussian filtering. The inverse FFT is then applied to convert the filtered frequency domain data back to the spatial domain. Through comparative analysis of these filtering techniques, practitioners can select the most appropriate method based on noise characteristics and image preservation requirements, balancing between noise removal effectiveness and detail retention.