SIMULTANEOUSLY SPARSE SOLUTIONS TO LINEAR INVERSE PROBLEMS WITH MULTIPLE SYSTEM MATRICES AND A SINGLE OBSERVATION VECTOR.
SIMULTANEOUSLY SPARSE SOLUTIONS TO LINEAR INVERSE PROBLEMS WITH MULTIPLE SYSTEM MATRICES AND A SINGLE OBSERVATION VECTOR.
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DOI：
10.1137/080730822
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发表时间：
2010-01-20
期刊：
影响因子：
--
通讯作者：
Adalsteinsson E
中科院分区：
文献类型：
--
作者：
Zelinski AC;Goyal VK;Adalsteinsson E
将层析选择性磁共振成像(MRI)射频激励脉冲设计问题抽象为同时具有稀疏性约束的线性逆问题。将确定多个未知信号向量，其中每个未知信号向量通过不同的系统矩阵，并且将结果相加以产生单个观测向量。在给定矩阵和孤立观测的情况下，目标是找到一个同时稀疏的未知向量集合，以近似求解该系统。我们将其称为多系统单输出(MSSO)同时稀疏逼近问题。本文将MSSO问题与其他同时存在的稀疏性问题进行了对比，并对求解该问题的算法进行了初步探索。推导了基于凸松弛的贪婪算法和技术，并进行了实证比较。实验包括无噪声和有噪声环境下的稀疏模式恢复和磁共振射频脉冲的设计。
A problem that arises in slice-selective magnetic resonance imaging (MRI) radio-frequency (RF) excitation pulse design is abstracted as a novel linear inverse problem with a simultaneous sparsity constraint. Multiple unknown signal vectors are to be determined, where each passes through a different system matrix and the results are added to yield a single observation vector. Given the matrices and lone observation, the objective is to find a simultaneously sparse set of unknown vectors that approximately solves the system. We refer to this as the multiple-system single-output (MSSO) simultaneous sparse approximation problem. This manuscript contrasts the MSSO problem with other simultaneous sparsity problems and conducts an initial exploration of algorithms with which to solve it. Greedy algorithms and techniques based on convex relaxation are derived and compared empirically. Experiments involve sparsity pattern recovery in noiseless and noisy settings and MRI RF pulse design.
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影响因子：
3
作者：
Daubechies, I;Defrise, M;De Mol, C
通讯作者：
De Mol, C
影响因子：
5.4
作者：
Chen, Jie;Huo, Xiaoming
通讯作者：
Huo, Xiaoming
影响因子：
5.4
作者：
Cotter, SF;Rao, BD;Kreutz-Delgado, K
通讯作者：
Kreutz-Delgado, K
DOI：
10.1049/ip-vis:19990445
发表时间：
1999-10-01
期刊：
IEE PROCEEDINGS-VISION IMAGE AND SIGNAL PROCESSING
影响因子：
--
作者：
Cotter, SF;Adler, J;Kreutz-Delgado, K
通讯作者：
Kreutz-Delgado, K
影响因子：
2
作者：
DONOHO, DL
通讯作者：
DONOHO, DL