用快速哈达玛变换加速滤波反投影算法的滤波过程

为了加速滤波反投影算法的滤波过程，提出了用快速哈达玛变换(FHT)实现线性卷积的快速算法。分析了哈达玛变换的特点和快速算法的时间复杂度，设计了用FHT计算线性卷积的矩阵表达式，并推导出了哈达玛域滤波器的增益矩阵的求解公式，分析了该方法的加速原理及其适用条件。理论分析表明，该方法比FFT线性卷积法快了一倍。仿真实验表明，该方法在不影响图像重建精度的情况下，相对于FFT线性卷积法，将滤波过程的速度提高了近一倍。

Accelerate the Filtering Process of Filtered Back Projection Algorithm Using Fast Hadamard Transform

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.