In this paper we develop a novel computational sensing framework for sensing
and recovering structured signals. When trained on a set of representative
signals, our framework learns to take undersampled measurements and recover
signals from them using a deep convolutional neural network. In other words, it
learns a transformation from the original signals to a near-optimal number of
undersampled measurements and the inverse transformation from measurements to
signals. This is in contrast to traditional compressive sensing (CS) systems
that use random linear measurements and convex optimization or iterative
algorithms for signal recovery. We compare our new framework with
$\ell_1$-minimization from the phase transition point of view and demonstrate
that it outperforms $\ell_1$-minimization in the regions of phase transition
plot where $\ell_1$-minimization cannot recover the exact solution. In
addition, we experimentally demonstrate how learning measurements enhances the
overall recovery performance, speeds up training of recovery framework, and
leads to having fewer parameters to learn.

本文提出了一种新型的计算感知框架，以深度卷积神经网络为基础，通过学习从原始信号到少量欠采样信号的转换和从欠采样信号到原始信号的逆转换，实现了结构化信号的感知和恢复。通过与传统压缩感知方法相比较，实验证明所提出的方法在信号恢复的性能、训练速度和参数数量等方面都取得了优异的表现。

DeepCodec: 基于深度卷积神经网络的自适应感知与恢复

DeepCodec: Adaptive Sensing and Recovery via Deep Convolutional Neural  Networks

The implementation of computational sensing strategies often faces
calibration problems typically solved by means of multiple, accurately chosen
training signals, an approach that can be resource-consuming and cumbersome.
Conversely, blind calibration does not require any training, but corresponds to
a bilinear inverse problem whose algorithmic solution is an open issue. We here
address blind calibration as a non-convex problem for linear random sensing
models in which we aim to recover an unknown signal from its projections on
sub-Gaussian random vectors, each of which is subject to an unknown
multiplicative factor (gain). To solve this optimisation problem we resort to
projected gradient descent starting from a suitable initialisation. An analysis
of this algorithm allows us to show that it converges to the global optimum
provided a sample complexity requirement is met, i.e., relating convergence to
the amount of information collected during the sensing process. Finally, we
present some numerical experiments in which our algorithm allows for a simple
solution to blind calibration of sensor gains in computational sensing
applications.

本文研究了线性随机感知模型中的盲校准问题，并通过投影梯度下降算法实现全局最优解。实验表明该算法可以实现计算感知中传感器增益的盲校准。