We propose a novel method for compressed sensing recovery using untrained
deep generative models. Our method is based on the recently proposed Deep Image
Prior (DIP), wherein the convolutional weights of the network are optimized to
match the observed measurements. We show that this approach can be applied to
solve any differentiable linear inverse problem, outperforming previous
unlearned methods. Unlike various learned approaches based on generative
models, our method does not require pre-training over large datasets. We
further introduce a novel learned regularization technique, which incorporates
prior information on the network weights. This reduces reconstruction error,
especially for noisy measurements. Finally, we prove that, using the DIP
optimization approach, moderately overparameterized single-layer networks can
perfectly fit any signal despite the non-convex nature of the fitting problem.
This theoretical result provides justification for early stopping.

通过未经训练的深度生成模型提出一种新方法，解决压缩感知恢复问题，具有比以前的方法更好的性能，并且不需要大规模数据集的预训练。同时，结合了关于网络权重的先验知识的新型学习正则技术，减少了重建误差。最后，通过 DIP 优化方法，证明了适度超参数的单层神经网络可以完美拟合任何信号，这一理论结果为提前停止提供了依据。

使用深度图像先验和学习正则化的压缩感知技术

Compressed Sensing with Deep Image Prior and Learned Regularization

Despite our extensive knowledge of biophysical properties of neurons, there
is no commonly accepted algorithmic theory of neuronal function. Here we
explore the hypothesis that single-layer neuronal networks perform online
symmetric nonnegative matrix factorization (SNMF) of the similarity matrix of
the streamed data. By starting with the SNMF cost function we derive an online
algorithm, which can be implemented by a biologically plausible network with
local learning rules. We demonstrate that such network performs soft clustering
of the data as well as sparse feature discovery. The derived algorithm
replicates many known aspects of sensory anatomy and biophysical properties of
neurons including unipolar nature of neuronal activity and synaptic weights,
local synaptic plasticity rules and the dependence of learning rate on
cumulative neuronal activity. Thus, we make a step towards an algorithmic
theory of neuronal function, which should facilitate large-scale neural circuit
simulations and biologically inspired artificial intelligence.

研究单层神经元网络如何执行在线对称非负矩阵分解（SNMF）的假设，通过导出基于 SNMF 成本函数的在线算法，可以实现具有局部学习规则的生物学上可行的网络。该算法具有软聚类和稀疏特征发现能力，是一个阶段性的研究，可以促进大规模神经电路模拟和生物启发式人工智能。