Filtered Back Projection Program

In this implementation, the methodology employed involves generating projection data using the Radon transform function, followed by image reconstruction through a filtered back projection algorithm that incorporates both frequency-domain filtering and time-domain convolution filtering. This approach effectively reduces noise and artifacts while enhancing the quality of reconstructed images. Specifically, the frequency-domain filtering method operates in the Fourier domain to apply filters to projection data, eliminating high-frequency noise and artifacts through operations like ramp filtering or Shepp-Logan filtering implemented using FFT (Fast Fourier Transform) algorithms. The time-domain convolution filtering then performs back projection by convolving the filtered projection data with appropriate kernel functions (such as Ram-Lak or Hamming filters) and summing them across all angles to reconstruct the final image in spatial domain. By combining these two filtering techniques, the algorithm achieves more accurate and clearer reconstructed images that better meet practical requirements. Key implementation steps include: computing projection data via radon() function, applying frequency-domain filters using fft() and ifft() operations, performing convolution with optimized filter kernels, and final image reconstruction through back projection accumulation.