Compressive sensing (CS) is a new approach for the acquisition and recovery
of sparse signals and images that enables sampling rates significantly below
the classical Nyquist rate. Despite significant progress in the theory and
methods of CS, little headway has been made in compressive video acquisition
and recovery. Video CS is complicated by the ephemeral nature of dynamic
events, which makes direct extensions of standard CS imaging architectures and
signal models difficult. In this paper, we develop a new framework for video CS
for dynamic textured scenes that models the evolution of the scene as a linear
dynamical system (LDS). This reduces the video recovery problem to first
estimating the model parameters of the LDS from compressive measurements, and
then reconstructing the image frames. We exploit the low-dimensional dynamic
parameters (the state sequence) and high-dimensional static parameters (the
observation matrix) of the LDS to devise a novel compressive measurement
strategy that measures only the dynamic part of the scene at each instant and
accumulates measurements over time to estimate the static parameters. This
enables us to lower the compressive measurement rate considerably. We validate
our approach with a range of experiments involving both video recovery, sensing
hyper-spectral data, and classification of dynamic scenes from compressive
data. Together, these applications demonstrate the effectiveness of the
approach.

本文提出了一种基于线性动态系统的视频压缩感知恢复框架，将视频恢复问题简化为先从压缩测量中估计 LDS 模型参数，然后重建图像帧。利用 LDS 的低维动态参数和高维静态参数来设计一种新颖的压缩测量策略，它只在每个时刻测量场景的动态部分并随时间累积以估计静态参数，并有效地降低了压缩测量率。经过各种实验验证了方法的有效性，包括视频恢复、感知高光谱数据以及从压缩数据中对动态场景进行分类。

动态场景的压缩采集

Compressive Acquisition of Dynamic Scenes

Recovery of the sparsity pattern (or support) of an unknown sparse vector
from a small number of noisy linear measurements is an important problem in
compressed sensing. In this paper, the high-dimensional setting is considered.
It is shown that if the measurement rate and per-sample signal-to-noise ratio
(SNR) are finite constants independent of the length of the vector, then the
optimal sparsity pattern estimate will have a constant fraction of errors.
Lower bounds on the measurement rate needed to attain a desired fraction of
errors are given in terms of the SNR and various key parameters of the unknown
vector. The tightness of the bounds in a scaling sense, as a function of the
SNR and the fraction of errors, is established by comparison with existing
achievable bounds. Near optimality is shown for a wide variety of practically
motivated signal models.

本文考虑了高维设置下的稀疏向量，研究在测量速率和样品的信噪比为有限常数的情况下，稀疏模式估计的误差比例将为常数分数，并且通过与现有可实现界的比较，建立了在比例误差和信噪比的功能下的范围上限。