Neural network learning of improved compressive sensing sampling and receptive field structure
Neural network learning of improved compressive sensing sampling and receptive field structure
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DOI：
10.1016/j.neucom.2021.05.061
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发表时间：
2021-06-07
期刊：
影响因子：
6
通讯作者：
Barranca, Victor J.
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文献类型：
--
作者：
Barranca, Victor J.
虽然现代信号处理中的压缩感知（CS）理论通常表明均匀随机采样有助于有效恢复稀疏信号，但这种测量在许多工程应用中是不可行的，并且不能很好地反映自然系统（包括大脑中的神经元网络）的约束。均匀随机采样也不利用许多类信号的底层结构，因此在这些情况下可能是次优的。我们通过制定一个新的神经网络框架来解决这些问题，该框架用于基于训练信号类中存在的内在结构来学习改进的CS采样。除了在适当的域中的稀疏性之外，这种方法不假设任何特定信号统计的知识，并且纯粹是数据驱动的。该学习方法是生物学上现实的，因为它利用（1）神经网络中的非对称反馈和前馈连接，以及（2）在训练CS测量矩阵时仅利用来自相邻层的信息。观察广泛的学习采样范例，提高CS信号重建相对于均匀随机采样，我们的学习采样广泛适用于整个后勤约束。受感官系统的感受野结构的启发，我们专门分析了自然场景的输入，并证明了改进的CS重建作为训练的结果，在几个选择的惩罚方案的采样权重。考虑到这种学习即使在稀疏和空间局部化的约束下也是有效的，正如在大脑中通常观察到的那样，我们假设神经元连接可能已经表现出了通过利用其稀疏结构来提供数据的压缩编码的目的，从而实现有效的信号传输。CO 2021 Elsevier B.V.保留所有权利。
While the theory of compressive sensing (CS) in modern signal processing typically indicates that uniformly random sampling facilitates the efficient recovery of sparse signals, such measurements are infeasible in many engineering applications and are not well reflected by the constraints of natural systems, including neuronal networks in the brain. Uniformly random sampling also does not leverage the underlying structure of many classes of signals, and may therefore be suboptimal in these cases. We address these issues by formulating a novel neural network framework for learning improved CS sampling based on the intrinsic structure present in classes of training signals. Beyond sparsity in an appropriate domain, this approach does not assume knowledge of any specific signal statistics and is purely data-driven. The learning methodology is biologically realistic in that it utilizes (1) asymmetric feedback and feedforward connections in the neural network and (2) only information from adjacent layers in training the CS measurement matrix. Observing a broad spectrum of learned sampling paradigms that improve CS signal reconstructions relative to uniformly random sampling, our learned sampling is widely applicable across logistical constraints. Motivated by the receptive field structure of sensory systems, we specifically analyze natural scene inputs and demonstrate improved CS reconstruction as a result of training across several choices of penalization schemes on the sampling weights. Considering this learning is effective even under sparse and spatially localized constraints, as commonly observed in the brain, we hypothesize that neuronal connectivity may have manifested with the aim of providing a compressive encoding of data by leveraging its sparse structure, thereby achieving efficient signal transmission. CO 2021 Elsevier B.V. All rights reserved.