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2010

Simultaneously Sparse Solutions to Linear Inverse Problems with Multiple System Matrices and a Single Observation Vector

8 years 1 months ago
Simultaneously Sparse Solutions to Linear Inverse Problems with Multiple System Matrices and a Single Observation Vector
Abstract. A problem that arises in slice-selective magnetic resonance imaging (MRI) radiofrequency (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 desi...
Adam C. Zelinski, Vivek K. Goyal, Elfar Adalsteins
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Where SIAMSC
Authors Adam C. Zelinski, Vivek K. Goyal, Elfar Adalsteinsson
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