信号处理中的反卷积计算

基于兄环圆卷积矩阵的逆阵仍是兄环圆卷积矩阵的原理，给出了一种采用快速离散傅里叶变换（FFT）的反卷积计算方法．对于N维圆卷积矩阵，所需复乘／除次数约为N（log2N＋1），复加次数约为2Nlog2N+■.文中还对卷积矩阵维数N=2c的反卷积计算进行了讨率。在不用FFT情况下，可将N维圆卷积矩阵求逆转变成解■，■，■…2阶线性方程组，所需乘法次数约为■．与传统算法相比，文中给出的算法，乘法次数少，计算速度快，易在实时快速信号处理中应用．

Computational methods in super-resolution microscopy

The broad applicability of super-resolution microscopy has been widely demonstrated in various areas and disciplines. The optimization and improvement of algorithms used in super-resolution microscopy are of great importance for achieving optimal quality of super-resolution imaging. In this review, we comprehensively discuss the computational methods in different types of super-resolution microscopy, including deconvolution microscopy, polarization-based super-resolution microscopy, structured illumination microscopy, image scanning microscopy, super-resolution optical fluctuation imaging microscopy, single-molecule localization microscopy, Bayesian super-resolution microscopy, stimulated emission depletion microscopy, and translation microscopy. The development of novel computational methods would greatly benefit super-resolution microscopy and lead to better resolution, improved accuracy, and faster image processing.