Performance Analysis of Joint-Sparse Recovery from Multiple Measurement Vectors via Convex Optimization: Which Prior Information is Better?
In sparse signal recovery of compressive sensing, the phase transition determines the edge, which separates successful recovery and failed recovery. The phase transition can be seen as an indicator and an intuitive way to judge, which recovery performance is better. Traditionally, the multiple measu...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2018-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8253453/ |
| _version_ | 1819163085884096512 |
|---|---|
| author | Shih-Wei Hu Gang-Xuan Lin Sung-Hsien Hsieh Chun-Shien Lu |
| author_facet | Shih-Wei Hu Gang-Xuan Lin Sung-Hsien Hsieh Chun-Shien Lu |
| author_sort | Shih-Wei Hu |
| collection | DOAJ |
| description | In sparse signal recovery of compressive sensing, the phase transition determines the edge, which separates successful recovery and failed recovery. The phase transition can be seen as an indicator and an intuitive way to judge, which recovery performance is better. Traditionally, the multiple measurement vectors (MMVs) problem is usually solved via ℓ<sub>2,1</sub>-norm minimization, which is our first investigation via conic geometry in this paper. Then, we are interested in the same problem but with two common constraints (or prior information): prior information relevant to the ground truth and the inherent low rank within the original signal. To figure out which constraint is most helpful, the MMVs problems are solved via ℓ<sub>2,1</sub>-ℓ<sub>2,1</sub> minimization and ℓ<sub>2,1</sub>-low rank minimization, respectively. By theoretically presenting the necessary and sufficient condition of successful recovery from MMVs, we can have a precise prediction of phase transition to judge, which constraint or prior information is better. All our findings are verified via simulations and show that, under certain conditions, ℓ<sub>2,1</sub>-ℓ<sub>2,1</sub> minimization outperforms ℓ<sub>2,1</sub>-low rank minimization. Surprisingly, ℓ<sub>2,1</sub>-low rank minimization performs even worse than ℓ<sub>2,1</sub>-norm minimization. To the best of our knowledge, we are the first to study the MMVs problem under different prior information in the context of compressive sensing. |
| first_indexed | 2024-12-22T17:38:32Z |
| format | Article |
| id | doaj.art-19e5672d1dc8428fa1ab658bc78a6a7a |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-22T17:38:32Z |
| publishDate | 2018-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-19e5672d1dc8428fa1ab658bc78a6a7a2022-12-21T18:18:28ZengIEEEIEEE Access2169-35362018-01-0163739375410.1109/ACCESS.2018.27915808253453Performance Analysis of Joint-Sparse Recovery from Multiple Measurement Vectors via Convex Optimization: Which Prior Information is Better?Shih-Wei Hu0Gang-Xuan Lin1Sung-Hsien Hsieh2Chun-Shien Lu3https://orcid.org/0000-0002-5900-0019Department of Computer Science and Information Engineering, National Taiwan University, Taipei, TaiwanDepartment of Mathematics, National Cheng-Kung University, Tainan City, TaiwanDepartment of Communications Engineering, National Taiwan University, Taipei, TaiwanAcademia Sinica, Institute of Information Science, Taipei, TaiwanIn sparse signal recovery of compressive sensing, the phase transition determines the edge, which separates successful recovery and failed recovery. The phase transition can be seen as an indicator and an intuitive way to judge, which recovery performance is better. Traditionally, the multiple measurement vectors (MMVs) problem is usually solved via ℓ<sub>2,1</sub>-norm minimization, which is our first investigation via conic geometry in this paper. Then, we are interested in the same problem but with two common constraints (or prior information): prior information relevant to the ground truth and the inherent low rank within the original signal. To figure out which constraint is most helpful, the MMVs problems are solved via ℓ<sub>2,1</sub>-ℓ<sub>2,1</sub> minimization and ℓ<sub>2,1</sub>-low rank minimization, respectively. By theoretically presenting the necessary and sufficient condition of successful recovery from MMVs, we can have a precise prediction of phase transition to judge, which constraint or prior information is better. All our findings are verified via simulations and show that, under certain conditions, ℓ<sub>2,1</sub>-ℓ<sub>2,1</sub> minimization outperforms ℓ<sub>2,1</sub>-low rank minimization. Surprisingly, ℓ<sub>2,1</sub>-low rank minimization performs even worse than ℓ<sub>2,1</sub>-norm minimization. To the best of our knowledge, we are the first to study the MMVs problem under different prior information in the context of compressive sensing.https://ieeexplore.ieee.org/document/8253453/Sparse representation<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₂,₁-norm minimizationmultiple-measurement vectorstatistical dimensioncompressed sensingconvex optimization |
| spellingShingle | Shih-Wei Hu Gang-Xuan Lin Sung-Hsien Hsieh Chun-Shien Lu Performance Analysis of Joint-Sparse Recovery from Multiple Measurement Vectors via Convex Optimization: Which Prior Information is Better? IEEE Access Sparse representation <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₂,₁-norm minimization multiple-measurement vector statistical dimension compressed sensing convex optimization |
| title | Performance Analysis of Joint-Sparse Recovery from Multiple Measurement Vectors via Convex Optimization: Which Prior Information is Better? |
| title_full | Performance Analysis of Joint-Sparse Recovery from Multiple Measurement Vectors via Convex Optimization: Which Prior Information is Better? |
| title_fullStr | Performance Analysis of Joint-Sparse Recovery from Multiple Measurement Vectors via Convex Optimization: Which Prior Information is Better? |
| title_full_unstemmed | Performance Analysis of Joint-Sparse Recovery from Multiple Measurement Vectors via Convex Optimization: Which Prior Information is Better? |
| title_short | Performance Analysis of Joint-Sparse Recovery from Multiple Measurement Vectors via Convex Optimization: Which Prior Information is Better? |
| title_sort | performance analysis of joint sparse recovery from multiple measurement vectors via convex optimization which prior information is better |
| topic | Sparse representation <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">l</italic>₂,₁-norm minimization multiple-measurement vector statistical dimension compressed sensing convex optimization |
| url | https://ieeexplore.ieee.org/document/8253453/ |
| work_keys_str_mv | AT shihweihu performanceanalysisofjointsparserecoveryfrommultiplemeasurementvectorsviaconvexoptimizationwhichpriorinformationisbetter AT gangxuanlin performanceanalysisofjointsparserecoveryfrommultiplemeasurementvectorsviaconvexoptimizationwhichpriorinformationisbetter AT sunghsienhsieh performanceanalysisofjointsparserecoveryfrommultiplemeasurementvectorsviaconvexoptimizationwhichpriorinformationisbetter AT chunshienlu performanceanalysisofjointsparserecoveryfrommultiplemeasurementvectorsviaconvexoptimizationwhichpriorinformationisbetter |