论文标题
盲层解卷
Blind hierarchical deconvolution
论文作者
论文摘要
反卷积是信号处理中的基本反问题，也是从其噪声测量中恢复信号的原型模型。然而，大多数基于模型的反转技术都需要有关卷积内核的知识，才能恢复准确的重建，并需要先前关于信号规律性的先验假设。为了克服这些局限性，我们参数卷积内核和先前的长度尺度，然后在反转过程中共同估计。提出的盲目分层反卷积的框架可以准确地重建具有不同规律性和未知内核大小的功能，并且可以通过经验贝叶斯的两步过程有效地解决，在该过程中，首先要通过优化和其他未知数来估算超套筒，然后通过分析公式进行估算。
Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the convolution kernel to recover an accurate reconstruction and additionally prior assumptions on the regularity of the signal are needed. To overcome these limitations, we parametrise the convolution kernel and prior length-scales, which are then jointly estimated in the inversion procedure. The proposed framework of blind hierarchical deconvolution enables accurate reconstructions of functions with varying regularity and unknown kernel size and can be solved efficiently with an empirical Bayes two-step procedure, where hyperparameters are first estimated by optimisation and other unknowns then by an analytical formula.
