稀疏字典基于的动态反问题求解
Sparse Dictionary-Based Solution of Dynamic Inverse Problems
AI总结：
本文提出了一种基于稀疏字典的动态反问题求解方法，通过随机分层稀疏先验和迭代交替序列算法，提升了解的稀疏性和计算效率，适用于压缩感知场景。
摘要：
在病态的动态反问题中，预期的空间特征和帧间的时间相关性可以被利用以提高计算解的质量，特别是当可用数据有限且未知数的维度较大时。一种利用空间和时间特性来表征解的方法是将这些特性编码到字典的条目中，并将解视为字典原子的稀疏线性组合。为了促进系数向量中大部分消失的条目，我们考虑了一种字典编码问题模型的随机扩展，其中包含一个随机的分层稀疏促进先验。我们使用迭代交替序列算法（IAS）计算系数向量的最大后验（MAP）估计，该算法已被证明能高效地解决反问题，并且对参数调节的需求极低。所提出的方法在真实世界动态计算机断层扫描和磁共振成像数据集上进行测试，其中它与流行的交替方向最小化方法（ADMM）进行了比较。计算示例表明，所提出的方法在压缩感知中与ADMM具有竞争力，但对超参数选择的敏感性显著降低。
英文摘要：
In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the dimensionality of the unknown is large. One way to take advantage of the spatial and temporal traits believed to characterize the solution is to encode them into the entries of a dictionary, and to seek the solution as a sparse linear combination of the dictionary atoms. To promote a vector of coefficients with mostly vanishing entries, we consider a stochastic extension of the dictionary coding problem model with a random hierarchical sparsity promoting prior. We compute the Maximum A Posteriori (MAP) estimate of the coefficient vector using the Iterative Alternating Sequential Algorithm (IAS), which has been demonstrated to efficiently solve inverse problems with minimal need for parameter tuning. The proposed methodology is tested on real-world dynamic Computed Tomography and MRI datasets, where it is compared to the popular Alternating Direction Method of Minimizers (ADMM). The computed examples show the that proposed methodology is competitive with the ADMM for compressed sensing, with a significantly lower sensitivity to hyper-parameter selection.
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