通过特征矩阵在未知噪声水平下进行稀疏自由反卷积

未知高斯噪声下的流形假设：条件证书与一致维数估计

Manifold Hypothesis: Conditional Certificates and Consistent Intrinsic Dimension Estimation

本文在未知高斯噪声下研究流形假设，提出条件证书方法，改进维数估计的样本条件，并证明一致维数估计，实验验证了方法的有效性。

Unknown sparsity in compressed sensing: Denoising and inference

The theory of Compressed Sensing (CS) asserts that an unknown signal $x\in\mathbb{R}^p$ can be accurately recovered from an underdetermined set of $n$ linear measurements with $n\ll p$, provided that $x$ is sufficiently sparse. However, in applications, the degree of sparsity $\|x\|_0$ is typically unknown, and the problem of directly estimating $\|x\|_0$ has been a longstanding gap between theory and practice. A closely related issue is that $\|x\|_0$ is a highly idealized measure of sparsity, and for real signals with entries not equal to 0, the value $\|x\|_0=p$ is not a useful description …

多尺度分层分解在盲反卷积中的应用

Applications of multiscale hierarchical decomposition to blind deconvolution

针对盲图像反卷积这一高度不适定非线性逆问题，提出多尺度分层分解方法（MHDM），通过迭代求解带自适应参数的变分问题获取精细细节，建立收敛性，采用分数阶索伯列夫范数正则化并施加正性约束，减少参数调整且分解结果具解释性。

An ADMM-LAP method for total variation myopic deconvolution of adaptive optics retinal images

Adaptive optics (AO) corrected ood imaging of the retina is a popular technique for studying the retinal structure and function in the living eye. However, the raw retinal images are usually of poor contrast and the interpretation of such images requires image deconvolution. Different from standard deconvolution problems where the point spread function (PSF) is completely known, the PSF in these retinal imaging problems is only partially known which leads to the more complicated myopic (mildly blind) deconvolution problem. In this paper, we propose an efficient numerical scheme for solving thi…

一种用于自适应光学天文成像的收敛盲反卷积方法

A convergent blind deconvolution method for post-adaptive-optics astronomical imaging

本文提出了一种适用于受泊松噪声扰动数据的盲反卷积方法，采用广义Kullback-Leibler散度作为目标函数，通过非精确交替最小化方法解决非凸问题，具有全局收敛性，适用于非密集恒星团的重建。

Guaranteed blind deconvolution and demixing via hierarchically sparse reconstruction

The blind deconvolution problem amounts to reconstructing both a signal and a filter from the convolution of these two. It constitutes a prominent topic in mathematical and engineering literature. In this work, we analyze a sparse version of the problem: The filter $h\in \mathbb{R}^μ$ is assumed to be $s$-sparse, and the signal $b \in \mathbb{R}^n$ is taken to be $σ$-sparse, both supports being unknown. We observe a convolution between the filter and a linear transformation of the signal. Motivated by practically important multi-user communication applications, we derive a recovery guarantee f…

快速且保证的盲多通道反卷积在双线性系统模型下

Fast and guaranteed blind multichannel deconvolution under a bilinear system model

本文研究了在双线性系统模型下，通过多个通道的输出估计每个通道的冲击响应，提出两种非凸优化方法并给出性能保证。

基于贝叶斯分解的贝索先验

Bayesian decomposition using Besov priors

本文提出基于贝索先验的贝叶斯分解方法，用于解决具有不同正则性的反问题，通过联合推断组件和超参数提升重建质量。

针对超出最小二乘的可分离逆问题的变量消去推广

A generalization of variable elimination for separable inverse problems beyond least squares

针对现有变量消去方法局限于最小二乘的缺陷，提出一种通用框架，通过修改标准优化方法模拟变量消去，适用于泊松似然、边界约束等问题，并在指数和拟合与盲反卷积测试中展现出速度和鲁棒性优势。