关于高斯低通滤波器的超分辨分析

对于经过高斯低通滤波的信号,通过求解一类凸优化模型稳定地恢复该信号的高频信息.当信号满足一定的分离条件时,给出了误差估计的界,从理论上证明了求解凸优化方法的稳定性.理论的证明依赖于压缩感知中的对偶理论.一个显著的差异在于高斯低通滤波器并不满足压缩感知中对于测量矩阵的要求,例如相关性,约束等距性质等.

The problem of super resolution with gaussian low pass filter

In this paper, for the signal which is convoluted by Gaussian low-pass filters, the high frequency information of the signal is recovered stably by solving a convex optimization model. When the signal satisfies a certain separation condition, the stability of the convex optimization problem is proved theoretically. The proof depends on the duality certification in compressed sensing. A significant difference is that Gaussian low-pass filters do not satisfy the conditions of measurement matrix in compressive sensing, such as mutual coherence, restricted isometry property, etc.