抛物线Radon变换中的参数采样与假频

抛物线Radon变换可作为消除多次波的一种非常有效的方法。在频率域对最小平方抛物线Radon变换中的曲率参数和偏移距参数的采样进行了研究 ,得到了保证方法稳定及抗假频的曲率参数的最小采样间隔和扫描范围 ,分析了由于偏移距采样不足造成的后果。研究表明 ,变换中曲率参数采样不足时 ,远炮检距数据道重建误差较大 ,采样过密只能稍微改善重建的结果 ,但会使最小平方反问题的方程组变为病态 ,而且还会增加计算机时。当偏移距采样不足时 ,整个变换过程不稳定 ,且会产生假频 ,表现为变换域中能量的发散 (拉伸 )。此外 ,若变换过程中曲率参数的扫描范围不能满足采样条件 ,变换时也会产生假频。利用数值计算对文中方法进行了验证。

Sampling and aliasing of parameters in parabolic Radon transform

Parabolic Radon transform (PRT) is a very effective method for eliminating the multiple waves. In the frequency domain, sampling of curvature and offset in least square PRT was investigated. The critical sampling interval of curvature and scanning range to guarantee the operation stability and anti aliasing were derived. The trouble resulted from sparse sampling in offset was analyzed. The results show that the reconstruction error for far offset will be great when under sampling of curvature. The least square problem will be ill conditioned, and the computer cost will increase with over sampling. The transform may be unstable so as to result in aliasing under the conditions of under sampling of offset and uncomfortable scanning scope of curvature. Modeling and real data examples proved the reasonability and stability of the presented sampling conditions.