Accelerate the Filtering Process of Filtered Back Projection Algorithm Using Fast Hadamard Transform
用快速哈达玛变换加速滤波反投影算法的滤波过程

To speedup the filtering process of the Filtered Back Projection (FBP) algorithm, a fast linear convolution algorithm using Fast Hadamard Transform (FHT) is proposed. The characteristic of Hadamard transform and its time complexity is analyzed. The matrix expression of using FHT to calculate linear convolution is designed. The equation of the Hadamard filter gain matrix is deduced. The acceleration principle and applicable condition of the method are analyzed. Theoretical analysis demonstrates that the method is faster than the FFT-convolution method for one time. The simulation experiment demonstrates that the method can advanced the filtering speed for about one time compared to the FFT-convolution method in the condition of no impacting the reconstructed image’s precision.