子空间追踪用于压缩感知信号重建

按模式主成分子空间追踪与矩阵尖峰协方差模型

Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Model

本文提出按模式主成分子空间追踪（MOP-UP）框架，通过平均子空间捕获和交替投影提取矩阵数据行列两个维度的隐藏变化，并引入分块矩阵特征值扰动界证明其非渐近误差界，在模拟与真实数据上验证了有效性。

梯度硬阈值化追求用于稀疏约束优化

Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization

本文将硬阈值化追求算法推广到稀疏约束凸优化问题，通过梯度下降与硬阈值化步骤交替，证明其在收敛速度和参数估计精度上的强保证，并在稀疏逻辑回归和稀疏精度矩阵估计中优于现有方法。

压缩感知专题

Topics in Compressed Sensing

本文综述了压缩感知的两种主要稀疏恢复方法：L1最小化（如基追踪）和贪婪算法（如ROMP和CoSaMP），并介绍了ROMP和CoSaMP在保证和速度上的优势。

Compressive Sensing for cut improvement and local clustering

We show how one can phrase the cut improvement problem for graphs as a sparse recovery problem, whence one can use algorithms originally developed for use in compressive sensing (such as SubspacePursuit or CoSaMP) to solve it. We show that this approach to cut improvement is fast, both in theory and practice and moreover enjoys statistical guarantees of success when applied to graphs drawn from probabilistic models such as the Stochastic Block Model. Using this new cut improvement approach, which we call ClusterPursuit, as an algorithmic primitive we then propose new methods for local clusteri…

LASSO 的贪婪一面：通过基于损失函数的正交匹配追踪实现加权稀疏恢复的新算法

The greedy side of the LASSO: New algorithms for weighted sparse recovery via loss function-based orthogonal matching pursuit

本文提出基于损失函数推广 OMP 的加权稀疏恢复贪婪算法，给出多种加权 LASSO 形式的显式选择规则，并通过实验验证其继承 SR-LASSO 与 LAD-LASSO 的优良特性。

Minimax Isometry Method: A compressive sensing approach for Matsubara summation in many-body perturbation theory

We present a compressive sensing approach for the long standing problem of Matsubara summation in many-body perturbation theory. By constructing low-dimensional, almost isometric subspaces of the Hilbert space we obtain optimum imaginary time and frequency grids that allow for extreme data compression of fermionic and bosonic functions in a broad temperature regime. The method is applied to the random phase and self-consistent $GW$ approximation of the grand potential. Integration and transformation errors are investigated for Si and SrVO$_3$.

具有周期边界条件的高维扩散方程的压缩傅里叶配置方法

Compressive Fourier collocation methods for high-dimensional diffusion equations with periodic boundary conditions

针对高维周期边界扩散方程的维数灾难问题，提出压缩傅里叶配置方法，结合压缩感知与谱配置，利用蒙特卡洛采样和稀疏恢复技术逼近解，理论分析与实验均表明其误差可控且有效缓解维数灾难。

Optimization of Convex Functions with Random Pursuit

We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a randomly chosen one-dimensional subspace. This randomized method only uses zeroth-order information about the objective function and does not need any problem-specific parametrization. We prove convergence and give convergence rates for smooth objectives assuming that the one-dimensional optimization can be solved exactly or approximately by an oracle. A convenient…

Generalizing CoSaMP to Signals from a Union of Low Dimensional Linear Subspaces

The idea that signals reside in a union of low dimensional subspaces subsumes many low dimensional models that have been used extensively in the recent decade in many fields and applications. Until recently, the vast majority of works have studied each one of these models on its own. However, a recent approach suggests providing general theory for low dimensional models using their Gaussian mean width, which serves as a measure for the intrinsic low dimensionality of the data. In this work we use this novel approach to study a generalized version of the popular compressive sampling matching pu…