Fibonacci Fourier Transform and Sliding Window Filtering

This paper presents the new Fibonacci Fourier like transform algorithms. The proposed transforms render the relationship between Fibonacci numbers and the conventional discrete Fourier transform. An application, de-noising images, is demonstrated with the idea of the proposed transforms by sliding window filtering technique. Two filtering algorithms, sliding double window filtering and fusion sliding window filtering, are exploited to improve the quality of images. A noisy system is then transformed to a filtered system as a result by altering different parameters. The proposed methods comparing with the well-known Wiener filtering are promising to be good to reduce the Gaussian noises on images.