Hyperspectral Imaging (HSI) serves as an important technique in remote
sensing. However, high dimensionality and data volume typically pose
significant computational challenges. Band selection is essential for reducing
spectral redundancy in hyperspectral imagery while retaining intrinsic critical
information. In this work, we propose a novel hyperspectral band selection
model by decomposing the data into a low-rank and smooth component and a sparse
one. In particular, we develop a generalized 3D total variation (G3DTV) by
applying the $\ell_1^p$-norm to derivatives to preserve spatial-spectral
smoothness. By employing the alternating direction method of multipliers
(ADMM), we derive an efficient algorithm, where the tensor low-rankness is
implied by the tensor CUR decomposition. We demonstrate the effectiveness of
the proposed approach through comparisons with various other state-of-the-art
band selection techniques using two benchmark real-world datasets. In addition,
we provide practical guidelines for parameter selection in both noise-free and
noisy scenarios.

该研究提出了一种新的高光谱波段选择模型，通过将数据分解为低秩平滑组分和稀疏组分，采用广义三维总变差（G3DTV）和交替方向乘子法（ADMM）来提高计算效率和抑制空间 - 光谱平滑性，验证了该方法的有效性，并提供了参数选择的实用指南。

基于广义 3DTV 和张量 CUR 分解的高光谱波段选择

Hyperspectral Band Selection based on Generalized 3DTV and Tensor CUR  Decomposition

This paper studies offline reinforcement learning with linear function
approximation in a setting with decision-theoretic, but not estimation
sparsity. The structural restrictions of the data-generating process presume
that the transitions factor into a sparse component that affects the reward and
could affect additional exogenous dynamics that do not affect the reward.
Although the minimally sufficient adjustment set for estimation of full-state
transition properties depends on the whole state, the optimal policy and
therefore state-action value function depends only on the sparse component: we
call this causal/decision-theoretic sparsity. We develop a method for
reward-filtering the estimation of the state-action value function to the
sparse component by a modification of thresholded lasso in least-squares policy
evaluation. We provide theoretical guarantees for our reward-filtered linear
fitted-Q-iteration, with sample complexity depending only on the size of the
sparse component.

这篇论文研究了离线强化学习中带有判决论但非估计稀疏性的线性函数逼近。

基于奖励相关性过滤的线性离线强化学习

Reward-Relevance-Filtered Linear Offline Reinforcement Learning

Many applications in data analysis rely on the decomposition of a data matrix
into a low-rank and a sparse component. Existing methods that tackle this task
use the nuclear norm and L1-cost functions as convex relaxations of the rank
constraint and the sparsity measure, respectively, or employ thresholding
techniques. We propose a method that allows for reconstructing and tracking a
subspace of upper-bounded dimension from incomplete and corrupted observations.
It does not require any a priori information about the number of outliers. The
core of our algorithm is an intrinsic Conjugate Gradient method on the set of
orthogonal projection matrices, the so-called Grassmannian. Non-convex sparsity
measures are used for outlier detection, which leads to improved performance in
terms of robustly recovering and tracking the low-rank matrix. In particular,
our approach can cope with more outliers and with an underlying matrix of
higher rank than other state-of-the-art methods.

提出一种基于 Grassmannian 的内置共轭梯度方法，可以从不完整和受损观测中重构和跟踪上限维度的子空间，用于处理数据分析中的低秩矩阵和稀疏组件，采用非凸稀疏度量进行异常点检测，性能优于其他最先进的方法。

利用 L0 替代方法从不完整观测中实现鲁棒 PCA 和子空间跟踪

Robust PCA and subspace tracking from incomplete observations using  L0-surrogates

This paper is about a curious phenomenon. Suppose we have a data matrix,
which is the superposition of a low-rank component and a sparse component. Can
we recover each component individually? We prove that under some suitable
assumptions, it is possible to recover both the low-rank and the sparse
components exactly by solving a very convenient convex program called Principal
Component Pursuit; among all feasible decompositions, simply minimize a
weighted combination of the nuclear norm and of the L1 norm. This suggests the
possibility of a principled approach to robust principal component analysis
since our methodology and results assert that one can recover the principal
components of a data matrix even though a positive fraction of its entries are
arbitrarily corrupted. This extends to the situation where a fraction of the
entries are missing as well. We discuss an algorithm for solving this
optimization problem, and present applications in the area of video
surveillance, where our methodology allows for the detection of objects in a
cluttered background, and in the area of face recognition, where it offers a
principled way of removing shadows and specularities in images of faces.

本文介绍了一种名为主成分追踪的凸型优化方法，能在有噪声或缺损情况下准确分离一个 $ m * n $ 数据矩阵的低秩和稀疏成分，该方法有望应用于视频监控和人脸识别等领域。