Fast Hankel Transform Algorithm for Efficient Signal Processing

The Fast Hankel Transform Algorithm is a computational optimization technique designed to efficiently compute the Hankel transform, which is pivotal in signal processing and image reconstruction applications. The core innovation lies in converting the convolution operation inherent in the standard Hankel transform into a multiplication operation through strategic mathematical reformulation. This conversion leverages the computational advantages of Fast Fourier Transform (FFT) algorithms, enabling significant acceleration when implemented in programming languages like MATLAB or Python. Key implementation aspects include: - Utilizing Bessel function properties to rewrite the Hankel integral as a convolution - Applying Fourier transform pairs to convert the convolution into frequency-domain multiplication - Employing zero-padding and logarithmic sampling techniques to handle singularity points The algorithm typically achieves O(N log N) computational complexity compared to the O(N²) requirement of direct integration methods. Validation studies demonstrate sub-percentage error margins in numerical precision, making it reliable for scientific computing and engineering applications such as optical system modeling, seismic data analysis, and electromagnetic field simulations. The method's efficiency enables real-time processing of large datasets and facilitates iterative reconstruction algorithms in medical imaging systems.