Nonparametric Simultaneous Sparse Recovery: an Application to Source Localization

通过向量化 Hankel 提升实现同时盲解混与超分辨率

Simultaneous Blind Demixing and Super-resolution via Vectorized Hankel Lift

针对同时盲解混与超分辨率问题，本文基于未知点扩散函数的子空间假设，将其转化为低秩矩阵解混，并利用向量化 Hankel 矩阵结构提出凸恢复方法，给出精确恢复的样本条件且验证了性能与效率。

Enhancing simultaneous rational function recovery: adaptive error correction capability and new bounds for applications

In this work we present some results that allow to improve the decoding radius in solving polynomial linear systems with errors in the scenario where errors are additive and randomly distributed over a finite field. The decoding radius depends on some bounds on the solution that we want to recover, so their overestimation could significantly decrease our error correction capability. For this reason, we introduce an algorithm that can bridge this gap, introducing some ad hoc parameters that reduce the discrepancy between the estimate decoding radius and the effective error correction capability…

纠缠辅助量子局部恢复中可观测量与测量量子位的同时约简

Simultaneous Reduction of Observables and Measured Qudits in Entanglement-Assisted Quantum Local Recovery

本文提出一种线性代数程序，同时约简纠缠辅助量子纠错码中的可观测量与修复组，以最小规模纠正擦除，并给出特殊码的闭式上界及量子信息局部性对应物。

Simultaneous Sparse Approximation and Common Component Extraction using Fast Distributed Compressive Sensing

Simultaneous sparse approximation is a generalization of the standard sparse approximation, for simultaneously representing a set of signals using a common sparsity model. Generalizing the compressive sensing concept to the simultaneous sparse approximation yields distributed compressive sensing (DCS). DCS finds the sparse representation of multiple correlated signals using the common + innovation signal model. However, DCS is not efficient for joint recovery of a large number of signals since it requires large memory and computational time. In this paper, we propose a new hierarchical algorit…

通过结构化低秩张量恢复同时进行盲反卷积与相位恢复的景观分析

Landscape Analysis of Simultaneous Blind Deconvolution and Phase Retrieval via Structured Low-Rank Tensor Recovery

本文通过结构化低秩张量恢复框架分析同时盲反卷积与相位检索问题，引入易处理的张量感知替代模型，证明黎曼梯度下降在温和条件下线性收敛，并通过数值实验验证了理论结果。

Simultaneous Block-Sparse Signal Recovery Using Pattern-Coupled Sparse Bayesian Learning

In this paper, we consider the block-sparse signals recovery problem in the context of multiple measurement vectors (MMV) with common row sparsity patterns. We develop a new method for recovery of common row sparsity MMV signals, where a pattern-coupled hierarchical Gaussian prior model is introduced to characterize both the block-sparsity of the coefficients and the statistical dependency between neighboring coefficients of the common row sparsity MMV signals. Unlike many other methods, the proposed method is able to automatically capture the block sparse structure of the unknown signal. Our …

Exact simultaneous recovery of locations and structure from known orientations and corrupted point correspondences

Let $t_1,\ldots,t_{n_l} \in \mathbb{R}^d$ and $p_1,\ldots,p_{n_s} \in \mathbb{R}^d$ and consider the bipartite location recovery problem: given a subset of pairwise direction observations $\{(t_i - p_j) / \|t_i - p_j\|_2\}_{i,j \in [n_l] \times [n_s]}$, where a constant fraction of these observations are arbitrarily corrupted, find $\{t_i\}_{i \in [n_ll]}$ and $\{p_j\}_{j \in [n_s]}$ up to a global translation and scale. We study the recently introduced ShapeFit algorithm as a method for solving this bipartite location recovery problem. In this case, ShapeFit consists of a simple convex progra…

Simultaneous structures in convex signal recovery - revisiting the convex combination of norms

In compressed sensing one uses known structures of otherwise unknown signals to recover them from as few linear observations as possible. The structure comes in form of some compressibility including different notions of sparsity and low rankness. In many cases convex relaxations allow to efficiently solve the inverse problems using standard convex solvers at almost-optimal sampling rates. A standard practice to account for multiple simultaneous structures in convex optimization is to add further regularizers or constraints. From the compressed sensing perspective there is then the hope to als…

通过ℓ₁-最小化同时恢复具有稀疏输入的线性系统状态与输入的充要条件

Necessary and Sufficient Conditions for Simultaneous State and Input Recovery of Linear Systems with Sparse Inputs by $\ell_1$-Minimization

本文首次给出线性动力系统中稀疏输入存在唯一性及通过线性规划同时恢复未知初始状态和稀疏输入的充要条件，并提供基于系统参数的可解释恢复条件。

利用 Unlimited Sensing 解锁离网稀疏恢复：时间与幅度的同时超分辨

Unlocking Off-the-Grid Sparse Recovery with Unlimited Sensing: Simultaneous Super-Resolution in Time and Amplitude

针对低比特采集下强弱尖峰难以同时恢复的问题，提出基于 USF 模编码的离网稀疏恢复框架，实现时间与幅度联合超分辨，并通过仿真和硬件实验验证。