抑制复原图像振铃波纹的频域循环边界算法

Circulation edge algorithm in frequency domain to suppress the ringing ripples on the restored image

提出了一种基于W iener滤波的频域循环边界复原算法,并给出了有效的规整化表达式和信噪比估算方法.复原算法首先将原观测图像按反射对称的方式延拓,形成一个新的观测图像(称为延拓图像);然后,用W iener滤波算法复原延拓图像,并取延拓图像的复原图像的主值序列作为原观测图像的复原图像.对延拓图像在频域进行复原处理时,需要使用FFT(Fast Fourier Transform)技术,将延拓图像进行周期延拓,因其结合边界在垂直方向上的梯度为零,且边界平滑满足微分条件,抑制了复原图像的振铃波纹.复原过程中,将噪声与原始图像的功率谱之比规整化为原观测图像信噪比的函数.实验结果表明,该算法对周边区域梯度变化较大的观测图像复原效果较好.

A restoration approach of the circulation edge algorithm in frequency domain based on the Wiener filtering is proposed. The effective regularization expression and the estimation method of the signal to noise ratio（SNR） are presented. First, the original supervised image is extended with the reflection symmetry manner to a new supervised image （NSI）. Then, the NSI is restored by the Wiener filtering algorithm, and the primary value sequence of the image restored by the NSI is considered as the restored image which is corresponding to the original supervised image. When the NSI is restored in frequency domain, the fast Fourier transform （FFT） technique need to be used and the NSI is extended periodically. Thus the gradient on the extended edges in the orthogonal orientation is zero, and the differential condition is satisfied with the edge smoothness. Therefore, the ringing ripples produced by the sharp changes of the extended edge＇s gradient are suppressed. In the restoration process, the ratio of the noise power spectrum to the original image power spectrum is regularized to the function of the SNR of the original supervised image. The experimental results show that the restoration effect using this approach is better than the one using Wiener filtering for the supervised image having large gradient changes on the area near to its edges.