论文标题
基于梯度的离散结构化测量算子的学习信号恢复
Gradient-Based Learning of Discrete Structured Measurement Operators for Signal Recovery
论文作者
论文摘要
无数的信号处理应用程序包括重建来自少数间接线性测量值的信号。有效测量运算符的设计通常受到基础硬件和物理学的限制，构成了具有挑战性的甚至通常离散的优化任务。尽管已经证明了通过迭代恢复算法展开的基于梯度学习的潜力，但当一组可接受的测量运算符是结构化和离散的时，尚不清楚如何利用这项技术。我们通过将展开的优化与Gumbel Reparametization结合使用来解决这个问题，从而可以计算分类随机变量的低变异梯度估计。我们的方法是由GloDismo（基于离散结构化测量运算符的基于梯度学习）正式化的。这种新颖的方法是易于实现的，计算上有效的，并且由于其与自动分化的兼容性而可扩展。我们从经验上证明了Glodismo在几种原型信号恢复应用中的性能和灵活性，验证了学习的测量矩阵的表现优于基于随机化和离散优化基线的常规设计。
Countless signal processing applications include the reconstruction of signals from few indirect linear measurements. The design of effective measurement operators is typically constrained by the underlying hardware and physics, posing a challenging and often even discrete optimization task. While the potential of gradient-based learning via the unrolling of iterative recovery algorithms has been demonstrated, it has remained unclear how to leverage this technique when the set of admissible measurement operators is structured and discrete. We tackle this problem by combining unrolled optimization with Gumbel reparametrizations, which enable the computation of low-variance gradient estimates of categorical random variables. Our approach is formalized by GLODISMO (Gradient-based Learning of DIscrete Structured Measurement Operators). This novel method is easy-to-implement, computationally efficient, and extendable due to its compatibility with automatic differentiation. We empirically demonstrate the performance and flexibility of GLODISMO in several prototypical signal recovery applications, verifying that the learned measurement matrices outperform conventional designs based on randomization as well as discrete optimization baselines.
