Noise reduction algorithms using Fibonacci Fourier transforms

This paper presents the new Fibonacci Fourier-like transforms. The proposed transforms render the relationship between Fibonacci numbers and the conventional Discrete Fourier Transform. The fast Fibonacci Fourier transforms are also introduced with the use of the Kronecker product properties. The proposed transforms are applied to the problem of noise reduction with two new algorithms, sliding double window filtering and fusion sliding window filtering. The primary concept of sliding double window filtering is to process the noisy signals with nonoverlapped windows, while the primary concept of fusion sliding window filtering is to process the noisy signals with various weighted filtering methods and overlapped signal values. The results and analysis show the noise reduction of the given noisy gray level images. The proposed methods are compared with the well-known Wiener filtering using images that contain Gaussian noise with the range of variance between 0 and 0.3. The analysis shows by visual inspection that the noisy parts are smoothened while retaining natural edges.