Near-Optimal Sparse Recovery in the L1 Norm

2008 ◽  
Author(s):  
Piotr Indyk ◽  
Milan Ruzic
Keyword(s):  
Sparse Recovery ◽  
L1 Norm

scholarly journals Block-Sparse Recovery with Optimal Block Partition

2021 ◽  
Author(s):  
Hiroki Kuroda ◽  
Daichi Kitahara
Keyword(s):  
Penalty Function ◽  
A Priori ◽  
Convex Relaxation ◽  
Optimal Solution ◽  
Sparse Recovery ◽  
Sparse Signals ◽  
L1 Norm ◽  
Recovery Method ◽  
Block Partition ◽  
L2 Norm

This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown a priori. We first introduce a nonconvex penalty function, where the block partition is adapted for the signal of interest by minimizing the mixed l2/l1 norm over all possible block partitions. Then, by exploiting a variational representation of the l2 norm, we derive the proposed penalty function as a suitable convex relaxation of the nonconvex one. For a block-sparse recovery model designed with the proposed penalty, we develop an iterative algorithm which is guaranteed to converge to a globally optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method.

scholarly journals Block-Sparse Recovery with Optimal Block Partition

2021 ◽  
Author(s):  
Hiroki Kuroda ◽  
Daichi Kitahara
Keyword(s):  
Penalty Function ◽  
A Priori ◽  
Convex Relaxation ◽  
Optimal Solution ◽  
Sparse Recovery ◽  
Sparse Signals ◽  
L1 Norm ◽  
Recovery Method ◽  
Block Partition ◽  
L2 Norm

This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown a priori. We first introduce a nonconvex penalty function, where the block partition is adapted for the signal of interest by minimizing the mixed l2/l1 norm over all possible block partitions. Then, by exploiting a variational representation of the l2 norm, we derive the proposed penalty function as a suitable convex relaxation of the nonconvex one. For a block-sparse recovery model designed with the proposed penalty, we develop an iterative algorithm which is guaranteed to converge to a globally optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method.

scholarly journals Block-Sparse Recovery with Optimal Block Partition

2021 ◽  
Author(s):  
Hiroki Kuroda ◽  
Daichi Kitahara
Keyword(s):  
Penalty Function ◽  
A Priori ◽  
Convex Relaxation ◽  
Optimal Solution ◽  
Sparse Recovery ◽  
Sparse Signals ◽  
L1 Norm ◽  
Recovery Method ◽  
Block Partition ◽  
L2 Norm

This paper presents a convex recovery method for block-sparse signals whose block partitions are unknown a priori. We first introduce a nonconvex penalty function, where the block partition is adapted for the signal of interest by minimizing the mixed l2/l1 norm over all possible block partitions. Then, by exploiting a variational representation of the l2 norm, we derive the proposed penalty function as a suitable convex relaxation of the nonconvex one. For a block-sparse recovery model designed with the proposed penalty, we develop an iterative algorithm which is guaranteed to converge to a globally optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method.

SegOMP: Sparse Recovery with Fewer Measurements

2014 ◽  
Vol E97.A (3) ◽  
pp. 862-864 ◽  
Author(s):  
Li ZENG ◽  
Xiongwei ZHANG ◽  
Liang CHEN ◽  
Weiwei YANG
Keyword(s):  
Sparse Recovery

Sparse Index Clones via the Sorted L1-Norm

2019 ◽  
Author(s):  
Philipp Kremer ◽  
Damian Brzyski ◽  
Malgorzata Bogdan ◽  
Sandra Paterlini
Keyword(s):  
L1 Norm
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