A Sampling Theorem for Deconvolution in Two Dimensions

点源反卷积：采样定理与鲁棒性保证

Deconvolution of Point Sources: A Sampling Theorem and Robustness Guarantees

本文研究了一种凸优化方法，用于从非均匀采样中恢复点源叠加，通过建立最小化连续$\ell_1$范数的理论保证，确保在满足最小分离条件和每个点源附近至少有两个样本时实现精确恢复。

基于MCMC的盲伯努利-高斯反卷积的增强采样方案

Enhanced sampling schemes for MCMC based blind Bernoulli-Gaussian deconvolution

针对盲稀疏反卷积问题，提出并比较了两种新的MCMC采样方案：K元组吉布斯采样器和部分边缘化采样器，后者通过积分出高斯幅度提高效率，仿真验证了收敛速度优势。

Inverting Spectrogram Measurements via Aliased Wigner Distribution Deconvolution and Angular Synchronization

We propose a two-step approach for reconstructing a signal ${\bf x}\in\mathbb{C}^d$ from subsampled short-time Fourier transform magnitude (spectogram) measurements: First, we use an aliased Wigner distribution deconvolution approach to solve for a portion of the rank-one matrix ${\bf \widehat{\bf x}}{\bf \widehat{\bf x}}^{*}.$ Second, we use angular syncrhonization to solve for ${\bf \widehat{\bf x}}$ (and then for ${\bf x}$ by Fourier inversion). Using this method, we produce two new efficient phase retrieval algorithms that perform well numerically in comparison to standard approaches and a…

通过变量投影对多快照尖峰反卷积的凸性区域进行刻画

Characterization of the Basin of Convexity for Multi-Snapshot Spike Deconvolution via Variable Projection

研究多快照尖峰反卷积问题，采用变量投影公式将其转化为非凸最小二乘问题，刻画了目标函数凸性区域，证明估计器在不同噪声下的性质及梯度下降收敛性，数值实验验证了理论结果。

任意基中稳定重构的广义采样定理

A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases

提出在可分希尔伯特空间中，从任意Riesz基的足够多采样中稳定重构另一任意Riesz基中的向量的广义框架，扩展了Eldar等人的工作并解决了其不稳定性问题。

关于随机采样矩阵均匀恢复定理

On the Theorem of Uniform Recovery of Random Sampling Matrices

本文通过改进的常数和更明确的证明，研究了压缩感知中随机采样矩阵均匀恢复所需样本数的下界，并改进了限制等距常数条件。