论文标题
非均匀傅立叶采样优化的杂散最小化器
Spurious minimizers in non uniform Fourier sampling optimization
论文作者
论文摘要
信号/图像处理文献的最新趋势是对特定信号数据集的傅立叶采样方案的优化。在本文中，我们解释了为什么选择最佳的非笛卡尔傅立叶采样模式是一个困难的非概念问题，这是一个难以通过揭示两个优化问题的问题。第一个是存在一系列通用信号类别的伪装最小化组合数。第二个是高频消失的梯度效应。我们通过展示了使用大型数据集如何减轻第一效果并在实验上说明使用随机梯度算法具有可变度量的好处。
A recent trend in the signal/image processing literature is the optimization of Fourier sampling schemes for specific datasets of signals. In this paper, we explain why choosing optimal non Cartesian Fourier sampling patterns is a difficult nonconvex problem by bringing to light two optimization issues. The first one is the existence of a combinatorial number of spurious minimizers for a generic class of signals. The second one is a vanishing gradient effect for the high frequencies. We conclude the paper by showing how using large datasets can mitigate first effect and illustrate experimentally the benefits of using stochastic gradient algorithms with a variable metric.
