BACKPROJ Implementation Using Filtered and Unfiltered Backprojection Algorithms

BACKPROJ represents a versatile implementation methodology that utilizes either filtered or unfiltered backprojection algorithms to efficiently perform inverse Radon transforms. The core algorithm involves designing a frequency-domain filter (such as Ram-Lak, Shepp-Logan, or Cosine filters) that is multiplied with the Fast Fourier Transform (FFT) of input projections. A crucial implementation step involves zero-padding projections to the next power of 2 length before filtering, which serves dual purposes: preventing spatial domain aliasing artifacts and optimizing FFT computational efficiency through radix-2 algorithms. The filtering process typically employs frequency-domain multiplication using MATLAB's fft and ifft functions, followed by backprojection operations that redistribute filtered projections across the reconstruction grid using interpolation techniques. This approach achieves high reconstruction accuracy while significantly accelerating the transformation process through optimized FFT implementations and systematic projection handling. The algorithm structure allows customization through filter selection and padding parameters, making it adaptable to various medical imaging and tomography applications.