Computationally efficient filtered-backprojection algorithm for tomographic image reconstruction using Walsh transform

In this paper, we discuss the implementation of the filtered-backprojection (FBP) algorithm for tomographic image reconstruction using Walsh transform to exploit its fast computational ability. Walsh transform is the fastest unitary transform known so far. The major advantage of Walsh transform is that it involves only real additions and subtractions whereas Fourier transform involves complex multiplications and additions. Implementation of the proposed algorithm necessitates the design of an appropriate filter in Walsh domain. In this research, the known Fourier filter coefficients have been transformed into Walsh domain, thereby the 1 × N Fourier filter coefficients were converted into an N × N sparse matrix with nonzero elements in a special pattern. The proposed algorithm has been implemented by taken into account of the special nature of the Walsh domain filter coefficients and tested for its performance using the well-known ‘Shepp-Logan head phantom’ test image. The results demonstrate that the reconstruction strategy has comparable performance with a significant reduction of computing time. For example, with a 128 × 128-pixel image and 180 views, the speedup achieved is fourfold, with reconstructions qualitatively and visually the same as that of FBP algorithm in the Fourier domain.