信号分离中的不交稀疏性及在医学成像混合反问题中的应用
Disjoint sparsity for signal separation and applications to hybrid inverse problems in medical imaging
AI总结：
本文研究在已知信号和的条件下，利用两个不同字典的稀疏表示进行信号重建，提出不交稀疏性方法用于解决多测量混合反问题。
摘要：
本文的主要目标是从已知信号和 $h_{i}=f+g_{i}$ 的信息中重建信号 $f$ 和 $g_{i}$，假设 $f$ 和 $g_{i}$ 可以分别用两个不同字典 $A_{f}$ 和 $A_{g}$ 进行稀疏表示。该方法将著名的形态学组件分析推广到多测量设置。论文的主要结果表明，当有足够的不相干测量 $g_{i}$ 时，通过找到每个 $i$ 对于拼接字典 $[A_{f},A_{g}]$ 的稀疏表示，可以唯一且稳定地重建 $f$ 和 $g_{i}$。该方法应用于几种混合成像反问题的重建过程，其中内部数据被测量。这些测量通常由主要未知量乘以其他未知量组成，因此不交稀疏性方法可以直接应用。作为例子，本文展示了如何将该方法应用于定量超声波成像的重建，包括在 Grüneisen 参数、光吸收和扩散系数均未知的情况下。
英文摘要：
The main focus of this work is the reconstruction of the signals $f$ and $g_{i}$, $i=1,...,N$, from the knowledge of their sums $h_{i}=f+g_{i}$, under the assumption that $f$ and the $g_{i}$'s can be sparsely represented with respect to two different dictionaries $A_{f}$ and $A_{g}$. This generalizes the well-known "morphological component analysis" to a multi-measurement setting. The main result of the paper states that $f$ and the $g_{i}$'s can be uniquely and stably reconstructed by finding sparse representations of $h_{i}$ for every $i$ with respect to the concatenated dictionary $[A_{f},A_{g}]$, provided that enough incoherent measurements $g_{i}$ are available. The incoherence is measured in terms of their mutual disjoint sparsity. This method finds applications in the reconstruction procedures of several hybrid imaging inverse problems, where internal data are measured. These measurements usually consist of the main unknown multiplied by other unknown quantities, and so the disjoint sparsity approach can be directly applied. As an example, we show how to apply the method to the reconstruction in quantitative photoacoustic tomography, also in the case when the Grüneisen parameter, the optical absorption and the diffusion coefficient are all unknown.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
