Enhance Image Sampling with Fourier Interpolation and Optional Filtering

In image processing, there are situations where we need to resample images, but traditional resampling methods often cause distortion that compromises image quality. Fourier interpolation provides an effective solution by increasing the sampling rate while maintaining image integrity. Additionally, an optional filter can be implemented to further optimize image quality. Fourier interpolation works by performing interpolation in the frequency domain on sampled pixel data to generate additional pixel points. This method effectively increases image resolution while preserving quality, resulting in clearer and more detailed images. The implementation typically involves: 1. Applying Fourier transform to convert the image to frequency domain 2. Zero-padding the frequency spectrum to increase resolution 3. Applying inverse Fourier transform to return to spatial domain The optional filter enhances results by removing high-frequency noise, producing smoother and more realistic images. This can be implemented using frequency-domain filtering techniques such as: - Low-pass filters (Butterworth, Gaussian) to suppress high-frequency components - Custom frequency masks for targeted noise reduction The filter parameters can be adjusted based on specific image characteristics and noise patterns.