image-processing - 理想低通滤波器中的振铃效应

Question

在理想的低通/高通滤波器中振铃效应的实际原因是什么？ 高斯低通滤波器如何去除它？

Answer 1

我只会引用 Wikipedia因为我不愿意写关于振铃的科学出版物。

关于您的问题:高斯低通不会“消除”振铃。它不会引起振铃。

The main cause of ringing artifacts is due to a signal being bandlimited (specifically, not having high frequencies) or passed through a low-pass filter; this is the frequency domain description. In terms of the time domain, the cause of this type of ringing is the ripples in the sinc function which is the impulse response (time domain representation) of a perfect low-pass filter. Mathematically, this is called the Gibbs phenomenon.

In the time domain, the cause is an impulse response that oscillates, assuming negative values. This can be resolved by using a filter whose impulse response is non-negative and does not oscillate, but shares desired traits. For example, for a low-pass filter, the Gaussian filter is non-negative and non-oscillatory, hence causes no ringing. However, it is not as good as a low-pass filter: it rolls off in the passband, and leaks in the stopband: in image terms, a Gaussian filter "blurs" the signal, which reflects the attenuation of desired higher frequency signals in the passband. A general solution is to use a window function on the sinc filter, which cuts off or reduces the negative lobes: these respectively eliminate and reduce overshoot and ringing. Note that truncating some but not all of the lobes eliminates the ringing beyond that point, but does not reduce the amplitude of the ringing that is not truncated (because this is determined by the size of the lobe), and increases the magnitude of the overshoot if the last non-cut lobe is negative, since the magnitude of the overshoot is the integral of the tail, which is no longer canceled by positive lobes.